Covering radius 1985-1994

Applicable Algebra in Engineering, Communications and Computing

Volumn 8, Issue 3, 1997, Pages 173-239

  Cohen, G D ^a   Litsyn, S N ^b   Lobstein, A C ^c   Mattson Jr , H F ^d  

^a TELECOM PARISTECH   (France)

^b TEL AVIV UNIVERSITY   (Israel)

^c CNRS   (France)

^d Center for Science and Technology   (United States)

Author keywords

Amalgamated direct sum; BCH codes; Binary codes; Blockwise direct sum; Covering radius; Density of coverings; Dual distance; Excess method; Normality; Reed Muller codes; Sphere covering bound

Indexed keywords

BINARY CODES; CODES (SYMBOLS); DECISION TABLES; DECODING;

AMALGAMATED DIRECT SUM; COVERING RADIUS; EXCESS METHOD; REED MULLER CODES; SPHERE COVERING BOUND;

ALGEBRA;

EID: 0030698544     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002000050061     Document Type: Review

References (290)

1. Aarts, E. H. L., van Laarhoven, P. J. M.: Local search in coding theory. Discrete Mathematics 106-107, 11-18 (1992)
2. Adams, M. J.: Subcodes and covering radius. IEEE Trans. Inform. Theory 32, 700-701 (September 1986)
3. Alon, N., Spencer, J.: The probabilistic method. London. New York: Wiley 1992
4. Anderson, D. R.: A new class of cyclic codes. SIAM J. Appl. Math. 16, 181-197 (1968)
5. Assmus, E. F., Jr., Mattson, H. F., Jr.: Some 3-error correcting BCH codes have covering radius 5. IEEE Trans. Inform. Theory 22, 348-349 (May 1976)
6. Assmus, E. F., Jr., Pless. V. S.: On the covering radius of extremal self-dual codes. IEEE Trans. Inform. Theory 29, 359-363 (May 1983)
7. Barg, A. M.: At the dawn of the theory of codes. Mathematical Intelligencer 15, 20-26 (1993)
8. Beck, J., Fiala, T.: "Integer-making" theorems. Discrete Appl. Math. 3, 1-8 (1981)
9. Berlekamp, E. R., Welch, L. R.: Weight distribution of the cosets of the (32, 6) Reed-Muller code. IEEE Trans. Inform. Theory 18, 203-207 (January 1972)
10. Beveraggi, M., Cohen, G. D.: On the density of best coverings in Hamming spaces. Lecture Notes in Computer Science, vol. 311, pp. 39-44. Berlin, Heidelberg, New York: Springer 1988
11. Bhandari, M. C., Garg, M. S.: Comments on "On the covering radius of codes". IEEE Trans. Inform. Theory 36, 953-954 (July 1990)
12. Bhandari, M. C., Garg, M. S.: A note on the covering radius of optimum codes. Discrete Appl. Math. 33, 3-9 (1991)
13. Blass, U., Litsyn, S. N.: Several new lower bounds for football pool systems. Ars Combinatoria (to appear)
14. Blinovskii, V. M.: Bounds for codes in the case of list decoding of finite volume. Problemy Peredachi Informatsii 22, 11-25 (1986). Translated in: Problems Inform. Transmission 22(1), 7-19 (1986)
15. Blinovskii, V. M.: Bounds for codes in the case of list decoding of finite volume. Problemy Peredachi Informatsii 22, 11-25 (1986). Translated in: Problems Inform. Transmission 22(1), 7-19 (1986)
16. n. Problemy Peredachi Informatsii 23, 50-53 (1987). Translated in: Problems Inform. Transmission 23(2), 130-132 (1987)
17. n. Problemy Peredachi Informatsii 23, 50-53 (1987). Translated in: Problems Inform. Transmission 23(2), 130-132 (1987)
18. Blinovskii, V, M.: Asymptotically exact uniform bounds for spectra of cosets of linear codes. Problemy Peredachi Informatsii 26, 99-103 (1990). Translated in: Problems Inform. Transmission 26(1), 83-86 (1990)
19. Blinovskii, V, M.: Asymptotically exact uniform bounds for spectra of cosets of linear codes. Problemy Peredachi Informatsii 26, 99-103 (1990). Translated in: Problems Inform. Transmission 26(1), 83-86 (1990)
20. Blinovskii, V. M.: Covering the Hamming space with sets translated by linear code vectors. Problemy Peredachi Informatsii 26, 21-26 (1990). Translated in: Problems Inform. Transmission 26(3), 196-201 (1990).
21. Blinovskii, V. M.: Covering the Hamming space with sets translated by linear code vectors. Problemy Peredachi Informatsii 26, 21-26 (1990). Translated in: Problems Inform. Transmission 26(3), 196-201 (1990).
22. Blokhuis, A., Lam, C. W. H.: More coverings by rook domains. J. Combinatorial Theory, Ser. A 36, 240-244 (1984)
23. Brouwer, A. E., Shearer, J. B., Sloane, N. J. A., Smith, W. D.: A new table of constant weight codes. IEEE Trans. Inform. Theory 36, 1334-1380 (November 1990)
24. Brualdi, R. A., Cai, N., Pless, V. S.: Orphan structure of the first-order Reed-Muller codes. Discrete Mathematics 102, 239-247 (1992)
25. Brualdi, R. A., Pless, V. S.: Orphans of the first order Reed-Muller codes. IEEE Trans. Inform. Theory 36, 399-401 (March 1990)
26. Brualdi, R. A., Pless, V. S.: On the covering radius of a code and its subcodes. Discrete Mathematics 83, 189-199 (1990)
27. Brualdi, R. A., Pless, V. S.: On the length of codes with a given covering radius. In: Ray-Chaudhuri, D. (ed.) Coding Theory and Design Theory. Part I: Coding Theory, pp. 9-15. Berlin, Heidelberg, New York: Springer 1990
28. Brualdi, R. A., Pless, V. S.: Covering radius. In: Brualdi, R. A., Huffman, W. C., Pless, V. S. (eds.) Handbook of Coding Theory (to appear)
29. Brualdi, R. A., Pless, V. S., Wilson, R. M.: Short codes with a given covering radius. IEEE Trans. Inform. Theory 35, 99-109 (January 1989)
30. Busschbach, P. B., Gerretzen, M. G. L., van Tilborg, H. C. A.: On the covering radius of binary linear codes meeting the Griesmer bound. IEEE Trans. Inform. Theory 31, 465-468 (July 1985)
31. Calderbank, A. R.: Covering radius and the chromatic number of Kneser graphs. J. Combinatorial Theory, Ser. A 54, 129-131 (1990)
32. Calderbank, A. R.: Covering bounds for codes. J. Combinatorial Theory, Ser. A 60, 117-122 (1992)
33. Calderbank, A. R.: Covering machines. Discrete Mathematics 106-107, 105-110 (1992)
34. Calderbank, A. R., Sloane, N. J. A.: Inequalities for covering codes. IEEE Trans. Inform. Theory 34, 1276-1280 (September 1988)
35. Cao, H. T., Dougherty, R. L., Janwa, H.: A [55, 16, 19] binary Goppa code and related codes having large minimum distance. IEEE Trans. Inform. Theory 37, 1432-1433 (September 1991)
36. Carnielli, W. A.: On covering and coloring problems for rook domains. Discrete Mathematics 57, 9-16 (1985)
37. Carnielli, W. A.: Hyper-rook domain inequalities. Stud. Appl. Math. 82, 59-69 (1990)
38. Chen, W., Honkala, I. S.: Lower bounds for q-ary covering codes. IEEE Trans. Inform. Theory 36, 664-671 (May 1990)
39. Chvatal, V.: A greedy heuristic for the set-covering problem. Math. Operations Res. 4, 233-235 (1979)
40. Clayton, R. F.: Multiple packings and coverings in algebraic coding theory. Ph.D. Thesis, University of California in Los Angeles, United States, 62 p. (1987)
41. Clayton, R. F.: Perfect multiple coverings in metric schemes. In: Ray-Chaudhuri, D. (ed.) Coding Theory and Design Theory. Part I: Coding Theory, pp. 51-64. Berlin, Heidelberg, New York: Springer 1990
42. Cohen, G. D.: A nonconstructive upper bound on covering radius. IEEE Trans. Inform. Theory 29, 352-353 (May 1983)
43. Cohen, G. D.: Non-linear covering codes: a few results and conjectures. Lecture Notes in Computer Science, vol. 356. pp. 225-229. Berlin, Heidelberg, New York: Springer 1989.
44. Cohen, G. D., Frankl, P.: On cliques and partitions in Hamming spaces. Rapport Interne ENST-C-81007, Ecole Nationale Supérieure des Télécommunications. Paris, 8 p. (1981)
45. Cohen, G. D., Frankl, P.: On generalized perfect codes and Steiner systems. Ann. Discrete Math. 18, 197-200 (1983)
46. Cohen, G. D., Frankl, P.: Good coverings of Hamming spaces with spheres. Discrete Mathematics 56, 125-131 (1985)
47. Cohen, G. D., Godlewski, Ph., Merkx, F.: Linear binary codes for write-once memories. IEEE Trans. Inform. Theory 32, 697-700 (September 1986)
48. Cohen, G. D., Honkala, I. S., Litsyn, S. N.: On weighted coverings and packings with diameter one. CISM Courses and Lectures, vol. 339, pp. 43-49. Berlin, Heidelberg, New York: Springer 1993
49. Cohen, G. D., Honkala, I. S., Litsyn, S. N., Mattson, H. F., Jr.: Weighted coverings and packings. IEEE Trans. Inform. Theory 41, 1856-1867 (November 1995)
50. Cohen, G. D., Karpovsky, M. G., Mattson, H. F., Jr., Schatz, J. R.: Covering radius - survey and recent results. IEEE Trans. Inform. Theory 31, 328-343 (May 1985)
51. Cohen, G. D., Litsyn, S. N.: On the covering radius of Reed-Muller codes. Discrete Mathematics 106-107, 147-155 (1992)
52. Cohen, G. D., Litsyn, S. N., Mattson, H. F., Jr.: On perfect weighted coverings with small radius. Lecture Notes in Computer Science, vol. 573, pp. 32-41. Berlin, Heidelberg, New York: Springer 1992
53. Cohen, G. D., Litsyn, S. N., Mattson, H. F., Jr.: Binary perfect weighted coverings, I The linear case. In: Capocelli, DeSantis, Vaccaro (eds.) Sequences II, pp. 36-51. Berlin, Heidelberg, New York: Springer 1993
54. Cohen, G. D., Lobstein, A. C., Sloane, N. J. A.: Further results on the covering radius of codes. IEEE Trans. Inform. Theory 32, 680-694 (September 1986)
55. Cohen, G. D., Lobstein, A. C., Sloane, N. J. A.: On a conjecture concerning coverings of Hamming space. Lecture Notes in Computer Science, vol. 228, pp. 79-89. Berlin, Heidelberg, New York: Springer 1986
56. Cohen, G. D., Zémor, G.: An application of combinatorial group theory to coding. Ars Combinatoria 23-A, 81-89 (1987)
57. Davydov, A. A.: Construction of linear covering codes. Problemy Peredachi Informatsii 26, 38-55 (1990). Translated in: Problems Inform. Transmission 26(4), 317-331 (1990)
58. Davydov, A. A.: Construction of linear covering codes. Problemy Peredachi Informatsii 26, 38-55 (1990). Translated in: Problems Inform. Transmission 26(4), 317-331 (1990)
59. Davydov, A. A.: Constructions of codes with covering radius 2. Lecture Notes in Computer Science, vol. 573, pp. 23-31. Berlin, Heidelberg, New York: Springer 1992
60. Davydov, A. A., Drozhzhina-Labinskaya, A. Y.: Binary linear codes with covering radii 3 and 4. 2nd Internat. Workshop on Algebraic and Combinatorial Coding Theory, Abstracts of papers, pp. 56-57, Leningrad (1990)
61. Davydov, A. A., Drozhzhina-Labinskaya, A. Y.: Table and families of short [n, n-r] codes with a given covering radius R. Preprint (1990)
62. Davydov, A. A., Drozhzhina-Labinskaya, A. Y.: Constructions of binary linear covering codes. 3rd Internat. Workshop on Algebraic and Combinatorial Coding Theory, Abstracts of papers, pp. 51-54, Voneshta Voda (1992)
63. Davydov, A. A., Drozhzhina-Labinskaya, A. Y.: Constructions, families, and tables of binary linear covering codes. IEEE Trans. Inform. Theory 40, 1270-1279 (July 1994)
64. Deligne, P.: La conjecture de Weil I. Instil. Hautes Etudes Sci. Publ. Math. 43, 273-307 (1974)
65. Delorme, C., Solé, P.: Diameter, covering index, covering radius and eigenvalues. Europ. J. Combinatorics 12, 95-108 (1991)
66. Delsarte, P.: Four fundamental parameters of a code and their combinatorial significance. Inform. and Control 23, 407-438 (1973)
67. Delsarte, P., Piret, P.: Do most binary linear codes achieve the Goblick bound on the covering radius? IEEE Trans. Inform. Theory 32, 826-828 (November 1986)
68. Dodunekov, S. M.: Some quasi-perfect double error correcting codes. Problems Control Information Theory 15(5), 367-375 (1986)
69. Dodunekov, S. M., Manev, K. N., Tonchev, V. D.: On the covering radius of binary [14,6] codes containing the all-one vector. IEEE Trans. Inform. Theory 34, 591-593 (May 1988)
70. Dodunekov, S. M., Manev, N. L.: An improvement of the Griesmer bound for some small minimum distances. Discrete Appl. Math. 12, 103-114 (1985)
71. Dougherty, R., Janwa, H.: Covering radius computations for binary cyclic codes. Math. Comp. 57, 415-434 (July 1991)
72. Downie, D. E., Sloane, N. J. A.: The covering radius of cyclic codes of length up to 31. IEEE Trans. Inform. Theory 31, 446-447 (May 1985)
73. El Gamal, A. A., Hemachandra, L. A., Shperling, I., Wei, V. K.: Using simulated annealing to design good codes. IEEE Trans. Inform. Theory 33, 116-123 (January 1987)
74. El-Zahar, M. H., Khairat, M. K.: On the weight distribution of the coset leaders of the first-order Reed-Muller code. IEEE Trans. Inform. Theory 33, 744-747 (September 1987)
75. Etzion, T., Greenberg, G.: Constructions of perfect mixed codes and other covering codes. IEEE Trans. Inform. Theory 39, 209-214 (January 1993)
76. Etzion, T., Greenberg, G., Honkala. I. S.: Normal and abnormal codes. IEEE Trans. Inform. Theory 39, 1453-1456 (July 1993)
77. Etzion, T., Wei, V. K., Zhang, Z.: Bounds on the sizes of constant weight covering codes. Designs, Codes Cryptography 5(3), 217-239 (May 1995)
78. Fazekas, G., Levenshtein, V. I.: On upper bounds for code distance and covering radius of designs in polynomial metric spaces. Proc. Fifth Joint Soviet-Swedish Workshop on Information Theory, pp. 65-68, Moscow (1991)
79. Fellows, M. R.: Encoding graphs in graphs. Ph.D. Thesis, University of California, San Diego, United States, 112 p. (1985)
80. Fernandes, H., Rechtschaffen, E.: The football pool problem for 7 and 8 matches. J. Combinatorial Theory, Ser. A 35, 109-114 (1983)
81. Fishburn, P. C., Sloane, N. J. A.: The solution to Berlekamp's switching game. Discrete Mathematics 74, 263-290 (1989)
82. Frances, M., Litman, A.: On covering problems of codes. Technical Report No. 827, Technion, Haifa, Israel, 8 p. (July 1994)
83. Gabidulin, E. M., Davydov, A. A., Tombak, L. M.: Linear codes with covering radius 2 and other new covering codes. IEEE Trans. Inform. Theory 37, 219-224 (January 1991)
84. Gleason, A. M.: Weight polynomials of self-dual codes and the MacWilliams identities. Actes, Congrès Internat. Math. 3, 211-215 (1970)
85. Godlewski, Ph.: Wom-codes construits àpartir des codes de Hamming. Discrete Mathematics 65, 237-243 (1987)
86. Gorenstein, D., Peterson, W. W., Zierler, N.: Two-error correcting Bose-Chaudhury codes are quasi-perfect. Inform, and Control 3, 291-294 (1960)
87. Graham, R. L., Sloane, N. J. A.: On the covering radius of codes. IEEE Trans. Inform. Theory 31, 385-401 (May 1985)
88. Griesmer, J. H.: A bound for error-correcting codes. IBM J. Res. Develop. 4, 532-542 (1960)
89. Habsieger, L.: Lower bounds for q-ary coverings by spheres of radius 1. J. Combinatorial Theory, Ser. A 67, 199-222 (1994)
90. Habsieger, L.: Binary codes with covering radius one: some new lower bounds. Discrete Mathematics (to appear)
91. Habsieger, L.: Some new lower bounds for ternary covering codes. Electronic J. Combinatorics, http://ejc.math.gatech.edu:8080/Journal/Volume 3/festschnft.html (1996)
92. Habsieger, L.: A new lower bound for the football pool problem for 7 matches. Preprint
93. van der Ham, M. W.: Simulated annealing applied in coding theory. Master's Thesis, Eindhoven University of Technology, The Netherlands, 50 p. (1988)
94. Hämäläinen, H. O., Honkala, I. S., Kaikkonen, M. K., Litsyn, S. N.: Bounds for binary multiple covering codes. Designs, Codes Cryptography 3(3), 251-275 (July 1993)
95. Hämäläinen, H. O., Honkala, I. S., Litsyn, S. N., Östergård, P. R. J.: Bounds for binary codes that are multiple coverings of the farthest-off points. SIAM J. Discrete Mathematics 8, 196-207 (1995)
96. Hämäläinen, H. O., Honkala, I. S., Litsyn, S. N., Österg̊ard, P. R. J.: Football pools - A game for mathematicians. Am. Math. Monthly 102(7), 579-588 (1995)
97. Hämäläinen, H. O., Rankinen, S.: Upper bounds for football pool problems and mixed covering codes. J. Combinatorial Theory, Ser. A 56, 84-95 (1991)
98. Hammond, P.:q-coverings, codes, and line graphs. J. Combinatorial Theory, Ser. B 30, 32-35 (1981)
99. Hartman, A., Mills, W. H., Mullin, R. C.: Covering triples by quadruples: an asymptotic solution. J. Combinatorial Theory, Ser. A 41, 117-138 (1986)
100. Hartman, A., Mullin, R. C., Stinson, D. R.: Exact covering configurations and Steiner systems. J. London Math. Soc. 25, 193-200 (1982)
101. Heden, O.: A generalized Lloyd theorem and mixed perfect codes. Matematiska Institutionen Stockholms Universitet, Memorandum No. 8 (1974)
102. Heden, O.: A new construction of group and nongroup perfect codes. Inform. and Control 34, 314-323 (1977)
103. m - 1 have covering radius 5. IEEE Trans. Inform. Theory 24, 257-258 (March 1978)
104. Helleseth, T.: On the covering radius of cyclic linear codes and arithmetic codes. Discrete Appl. Math. 11, 157-173 (1985)
105. Helleseth, T., Klove T., Mykkeltveit, J.: On the covering radius of binary codes. IEEE Trans. Inform. Theory 24, 627-628 (September 1978)
106. Helleseth, T., Mattson, H. F., Jr.: On the cosets of the simplex code. Discrete Mathematics 56, 169-189 (1985)
107. Herzog, M., Schönheim, J.: Linear and nonlinear single-error correcting perfect mixed codes. Inform, and Control 18, 364-368 (1971)
108. Herzog, M., Schönheim, J.: Group partition, factorization and the vector covering problem. Canad. Math. Bull. 15, 207-214 (1972)
109. Honkala, I. S.: On the intersections and unions of Hamming spheres. In: The Very Knowledge of Coding, Turku, Finland, pp. 70-81 (1987)
110. Honkala, I. S.: Bounds for binary constant weight and covering codes. Licentiate Thesis, University of Turku, Finland, 75 p. (1987)
111. Honkala, I. S.: Lower bounds for binary covering codes. IEEE Trans. Inform. Theory 34, 326-329 (March 1988)
112. Honkala, I. S.: Combinatorial bounds for binary constant weight and covering codes. Ph.D. Thesis, University of Turku, Finland, 108 p. (January 1989)
113. Honkala, I. S.: On the normality of codes with covering radius one. Proc. Fourth Joint Swedish-Soviet Workshop on Information Theory, pp. 223-226 (1989)
114. Honkala, I. S.: Modified bounds for covering codes. IEEE Trans. Inform. Theory 37, 351-365 (March 1991)
115. Honkala, I. S.: On (k, t )-subnormal covering codes. IEEE Trans. Inform. Theory 37, 1203-1206 (July 1991)
116. Honkala, I. S.: All binary codes with covering radius one are subnormal. Discrete Mathematics 94, 229-232 (1991)
117. Honkala, I. S.: On lengthening of covering codes. Discrete Mathematics 106-107, 291-295 (1992)
118. Honkala, I. S.: A Graham-Sloane type construction for s-surjective matrices. J. Algebr. Combinatorics 1, 347-351 (1992)
119. Honkala, I. S.: A lower bound on binary codes with covering radius one. Lecture Notes in Computer Science, vol. 781, pp. 34-37. Berlin, Heidelberg, New York: Springer 1994
120. Honkala, I. S.: On the normality of multiple covering codes. Discrete Mathematics 125, 229-239 (1994)
121. Honkala, I. S.: On (q, 1)-subnormal q-ary covering codes. Discrete Appl. Math. 152, 213-221 (1994)
122. Honkala, I. S.: A new lower bound on codes with covering radius one. Proc. Internat. Symposium Inform. Theory Appl. 1, 39-41, Sydney (1994)
123. Honkala, I. S.: On the early history of the ternary Golay code. Unpublished
124. Honkala, I. S., Hämäläinen. H. O.: A new construction for covering codes. IEEE Trans. Inform. Theory 34, 1343-1344 (September 1988)
125. Honkala, I. S., Hämäläinen. H. O.: Bounds for abnormal binary codes with covering radius one. IEEE Trans. Inform. Theory 37, 372-375 (March 1991)
126. Honkala, I. S., Kaipainen, Y., Tietäväinenm A.: Long binary narrow-sense BCH codes are normal. AAECC 8, 49-55
127. Honkala, I. S., Litsyn, S. N.: Generalizations of the covering radius problem in coding theory. Bull Internat. Combinatorial Association (to appear)
128. Honkala, I. S., Österg̊ard, P. R. J.: Applications in code design. In: Aarts, E. H. L., Lenstra, J. K. (eds.) Local Search Algorithms. Chap. 12, (to appear)
129. Honkala, I. S., Tietäväinen, A.: Codes and number theory. In: Brualdi, R. A., Huffman, W. C., Pless, V. S. (eds.) Handbook of Coding Theory (to appear)
130. van der Horst, J. A., Berger, T.: Complete decoding of triple-error-correcting binary BCH codes. IEEE Trans. Inform. Theory 22, 138-147 (March 1976)
131. Hou, X. D.: Covering radius and error correcting codes. Ph.D. Thesis, University of Illinois, Chicago, United States, 77 p. (1990)
132. Hou, X. D.: Some results on the norm of codes. IEEE Trans. Inform. Theory 36, 683-685 (May 1990)
133. Hou, X. D.: New lower bounds for covering codes. IEEE Trans. Inform. Theory 36, 895-899 (July 1990)
134. Hou, X. D.: An improved sphere covering bound for the codes with n = 3R + 2. IEEE Trans. Inform. Theory 36, 1476-1478 (November 1990)
135. Hou, X. D.: Binary linear quasi-perfect codes are normal. IEEE Trans. Inform. Theory 37, 378-379 (March 1991)
136. Hou, X. D.: On the covering radius of subcodes of a code. IEEE Trans. Inform. Theory 37, 1706-1707 (November 1991)
137. Hou, X. D.: Some results on the covering radii of Reed-Muller codes. IEEE Trans. Inform. Theory 39, 366-378 (March 1993)
138. Hou, X. D.: Further results on the covering radii of the Reed-Muller codes. Designs, Codes Cryptography 3(2), 167-177 (May 1993)
139. Hou, X. D.: The Reed-Muller code R(1.7) is normal. Designs. Codes Cryptography (to appear)
140. Hou, X. D.: The covering radius of R(1, 9) in R(4, 9). Designs, Codes Cryptography 8(3), 285-292 (June 1996)
141. Janwa, H.: Relations among parameters of codes. Ph.D. Thesis, Syracuse Univers, United States, 116 p. (1986)
142. Janwa, H.: Some new upper bounds on the covering radius of binary linear codes. IEEE Trans. Inform. Theory 35, 110-122 (January 1989)
143. Janwa, H.: Some optimal codes from algebraic geometry and their covering radii. Europ. J. Combinatorics 11, 249-266 (1990)
144. Janwa, H.: On the parameters of algebraic geometric codes. Lecture Notes in Computer Science, vol. 539, pp. 19-28. Berlin, Heidelberg, New York: Springer 1991.
145. Janwa, H., Mattson, H. F., Jr.: Covering radii of even subcodes of t-dense codes. Lecture Notes in Computer Science, vol. 229, pp. 120-130. Berlin, Heidelberg, New York: Springer 1986
146. Janwa, H., Mattson, H. F., Jr.: On the normality of binary linear codes. IEEE Trans. Inform. Theory (submitted)
147. Kabatianskii, G. A., Panchenko, V. I.: Unit sphere packings and coverings of the Hamming space. Problemy Peredachi Informatsii 24, 3-16 (1988). Translated in: Problems Inform. Transmission 24(4), 261-272 (1988)
148. Kabatianskii, G. A., Panchenko, V. I.: Unit sphere packings and coverings of the Hamming space. Problemy Peredachi Informatsii 24, 3-16 (1988). Translated in: Problems Inform. Transmission 24(4), 261-272 (1988)
149. Kalbfleisch, J. G., Stanton, R. G.: A combinatorial problem in matching. J. London Math. Soc. 44, 60-64 (1969)
150. Kamps, H. J. L., van Lint, J. H.: The football pool problem for 5 matches. J. Combinatorial Theory, Ser. A 3, 315-325 (1967)
151. Kamps, H. J. L., van Lint, J. H.: A covering problem. Combinatorial Theory Its Appl. II, pp. 679-685. In : Colloquia Mathematica Societatis Jànos Bolyai, Ser. 4 (1970)
152. Katsman, G. L.: Bounds on covering radius of dual product codes. Lecture Notes in Computer Science, vol. 573, pp. 52-57. Berlin, Heidelberg, New York: Springer 1992
153. Kilby, K. E., Sloane, N. J. A.: On the covering radius problem for codes: I Bounds on normalized covering radius, II Codes of low dimension; normal and abnormal codes. SIAM J. Algebraic Discrete Methods 8, 604-627 (1987)
154. Kirkpatrick, S., Gelatt, C. D., Jr., Vecchi, M. P.: Optimization by simulated annealing. Science 220, 671-680 (May 1983)
155. Kleitman, D. J.: On a combinatorial conjecture of Erdös. J. Combinatorial Theory 1, 209-214 (1966)
156. Kolev, E.: Codes over GF(3) of length 5, 27 codewords and covering radius I. J. Combinatorial Designs 1(4), 265-275 (1993)
157. Kolev, E., Landgev, I.: On some mixed covering codes of small length. Lecture Notes in Computer Science, vol. 781, pp. 38-50. Berlin, Heidelberg, New York: Springer 1994
158. Koschnick, K. U.: A new upper bound for the football pool problem for nine matches. J. Combinatorial Theory, Ser. A 62, 162-167 (1993)
159. van Laarhoven, P. J. M., Aarts, E. H. L., van Lint, J. H., Wille, L. T.: New upper bounds for the football pool problem for 6, 7 and 8 matches. J. Combinatorial Theory, Ser. A. 52, 304-312 (1989)
160. Laborde, J. M.: Une nouvelle famille de codes binaires, parfaits, non linéaires. ComptesRendus Académie Sciences, Ser. I 297, 67-70 (1983)
161. Laborde, J. M.: Sur le nombre domatique du n-cubeet une conjecture de Zelinka. Europ. J. Combinatorics 8, 175-177 (1987)
162. Lahtonen, J.: An optimal polynomial for a covering radius problem. Discrete Mathematics 105, 313-317 (1992)
163. Lang, S., Weil, A.: Number of points of varieties in finite fields. Am. J. Math. 76, 819-827 (1954)
164. Langevin, P.: The covering radius of RM(1, 9) into RM(3, 9). Lecture Notes in Computer Science, vol. 514, pp. 51-59. Berlin, Heidelberg, New York: Springer 1991
165. Lenstra, H. W., Jr.: Two theorems on perfect codes. Discrete Mathematics 3, 125-132 (1972)
166. Li, D., Chen W.: New lower bounds for binary covering codes. IEEE Trans. Inform. Theory 40, 1122-1129 (July 1994)
167. Lindström, B.: Group partitions and mixed perfect codes. Canad. Math. Bull, 18, 57-60 (1975)
168. van Lint, J. H.: A survey of perfect codes. Rocky Mountain J. Math. 5, 199-224 (1975)
169. van Lint, J. H.: Recent results on covering problems. Lecture Notes in Computer Science, vol. 357, pp. 7-21. Berlin, Heidelberg, New York: Springer 1989
170. van Lint, J. H., Jr.: Covering radius problems. Master's Thesis, Eindhoven University of Technology, The Netherlands, 41 p. (1988)
171. van Lint, J. H., Jr., van Wee, G. J. M.: Generalized bounds on binary-ternary mixed packing and covering codes. J. Combinatorial Theory, Ser. A 57, 130-143 (1991)
172. Litsyn, S. N., Moreno, C. J., Moreno. O.: Divisibility properties and new bounds for cyclic codes and exponential sums in one and several variables. AAECC 5, 105-116 (1994)
173. Litsyn, S., Tietäväinen, A.: Upper bounds on the covering radius of a code with a given dual distance. Europ. J. Combinatorics 17, 265-270 (1996)
174. 3(n, R) from linear inequalities. IEEE Trans. Inform. Theory (submitted)
175. Lobstein, A. C.: Contributions au codage combinatoire: ordres additifs, rayon de recouvrement. Thèse, Télécom Paris, France, 163 p. (1985)
176. Lobstein, A. C., Cohen, G. D., Sloane, N. J. A.: Recouvrements d'espaces de Hamming binaires. Comptes-Rendus l'Académie Sciences, Ser. I 301, 135-138 (1985)
177. Lobstein A., Pless, V. S., The length function: a revised table. Lecture Notes in Computer Science, vol. 781, pp. 51-55. Berlin, Heidelberg, New York: Springer 1994
178. Lobstein, A. C., van Wee. G. J. M.: On normal and subnormal q-ary codes. IEEE Trans. Inform. Theory 35, 1291-1295 (November 1989) and 36, 1498 (November 1990)
179. Lobstein, A. C., van Wee. G. J. M.: On normal and subnormal q-ary codes. IEEE Trans. Inform. Theory 35, 1291-1295 (November 1989) and 36, 1498 (November 1990)
180. Lovasz, L.: On the ratio of optimal integral and fractional covers. Discrete Mathematics 13, 383-390 (1975)
181. Lovasz, L.: Covers, packings, and some heuristic algorithms. Proc. 5th British Combinatorial Conf., pp. 417-429 (1975)
182. MacDonald, J. E.: Design methods for maximum minimum-distance error-correcting codes. IBM J. Res. Develop. 4, 43-57 (1960)
183. Mac Williams, F. J., Sloane, N. J. A.: The theory of error-correcting codes. Amsterdam. The Netherlands: North-Holland 1977
184. Maiorana, J. A.: A classification of the cosets of the Reed-Muller code K(1, 6). Math. Comp. 57, 403-414 (July 1991)
185. Mattson, H. F. Jr.: An upper bound on covering radius. Ann. Discrete Math. 17, 453-458 (1982)
186. Mattson, H. F., Jr.: Another upper bound on covering radius. IEEE Trans. Inform. Theory 29, 356-359 (May 1983)
187. Mattson, H. F., Jr.: An improved upper bound on covering radius. Lecture Notes in Computer Science, vol. 228, pp. 90-106. Berlin, Heidelberg, New York: Springer 1986
188. Mattson, H. F., Jr.: Simplifications to "A new approach to the covering radius. . .". J. Combinatorial Theory, Ser. A 57, 311-315 (July 1991)
189. Mattson, H. F., Jr., Schatz, J. R.: A brief survey of covering radius. Ann Discrete Math 18, 617-624 (1983)
190. Mauldon, J. G.: Covering theorems for groups. Quart. J. Math. Oxford 1, 284-287 (1950)
191. McLoughlin, A.: The covering radius of the (m - 3)rd order Reed-Muller codes and a lower bound on the (m - 4)th order Reed-Muller codes. SIAM J. Appl. Math. 37, 419-422 (1979)
192. McLoughlin, A.: The complexity of computing the covering radius of a code. IEEE Trans. Inform. Theory 30, 800-804 (November 1984)
193. Mills, W. H.: Covering designs I: Coverings by a small n umber of subsets. Ars Combinatoria 8, 199-315 (1979)
194. Mollard, M.: Les invariants du n-cube. Thèse de 3ème cycle. Université de Grenoble, France, 113 p. (1981)
195. Mollard, M.: Une nouvelle famille de 3-codes parfaits sur GF(q). Discrete Mathematics 49, 209-212 (1984)
196. Mollard, M.: A generalized parity function and its use in the construction of perfect codes. SIAM J. Algebraic Discrete Methods 7, 113-115 (1986)
197. Moreno, C. J., Moreno, O.: Exponential sums and Goppa codes I. Proc. Am. Math. Soc. 111, 523-531 (1991)
198. Moreno, C. J., Moreno, O.: Exponential sums and Goppa codes II. IEEE Trans. Inform. Theory 38, 1222-1229 (July 1992)
199. Moreno, O.: Personal communication (1992)
200. Moreno, O., Moreno. C. J.: Constructive elementary approach to the covering radius of long BCH codes. 2nd Internat. Workshop on Algebraic and Combinatorial Coding Theory, Abstracts of papers, pp. 162-165, Leningrad (1990)
201. Moreno O., Moreno C. J.: Constructive elementary approach to the covering radius of long BCH codes. Preprint
202. Mykkeltveit, J.: The covering radius of the (128.8) Reed-Muller code is 56. IEEE Trans. Inform. Theory 26, 359-362 (May 1980)
203. Nurmela, K. J.: Constructing combinatorial designs by local search. J. Sc. Thesis, Helsinki University of Technology, Research Report. Series A, No. 27, 76 p. (November 1993)
204. Nurmela, K. J., Österg̊ard, P. R. J.: Constructing covering designs by simulated annealing. Helsinki University of Technology, Technical Report, Series B, No. 10, 25 p. (January 1993)
205. Nurmela, K. J., Österg̊ard. P. R. J.: Upper bounds for covering designs by simulated annealing. Congressus Numerantium 96, 93-111 (1993)
206. Olson, J. E., Spencer, J.: Balancing families of sets. J. Combinatorial Theory, Ser. A 25, 29-37 (1978)
207. Österg̊ard, P. R. J.: A new binary code of length 10 and covering radius 1. IEEE Trans. Inform. Theory 37, 179-180 (January 1991)
208. Österg̊ard, P. R. J.: Upper bounds for q-ary covering codes. IEEE Trans. Inform. Theory 37, 660-664 (May 1991) and 37, 1738 (November 1991)
209. Österg̊ard, P. R. J.: Upper bounds for q-ary covering codes. IEEE Trans. Inform. Theory 37, 660-664 (May 1991) and 37, 1738 (November 1991)
210. Österg̊ard, P. R. J.: Constructions of mixed covering codes. Helsinki University of Technology, Research Report, Series A, No. 18, 44 p. (December 1991)
211. Österg̊ard, P. R. J.: Further results on (k, t)-subnormal covering codes. IEEE Trans. Inform. Theory 38, 206-210 (January 1992)
212. Österg̊ard, P. R. J.: Construction methods for covering codes. Ph.D. Thesis, Helsinki University of Technology, Research Report, Series A, No. 25, 107 p. (September 1993)
213. Österg̊ard, P. R. J.: New upper bounds for the football pool problem for 11 and 12 matches. J. Combinatorial Theory, Ser. A 67, 161-168 (1994)
214. Österg̊ard, P. R. J.: Construction methods for mixed covering codes. In: Gyllenberg, M., Persson, L. E. (eds.) Analysis, Algebra, Computers Math. Res., pp. 387-408. New York: Dekker 1994
215. Österg̊ard, P. R. J.: New constructions for q-ary covering codes. Discrete Mathematics (submitted)
216. Österg̊ard, P. R. J.: Constructing covering codes by tabu search. J. Combinatorial Designs (submitted)
217. Österg̊ard, P. R. J., Hämäläinen, H. O.: New upper bounds for binary-ternary mixed covering codes. Helsinki University of Technology, Research Report, Series A, No. 22, 33 p. (March 1993)
218. Österg̊ard, P. R. J., Hämäläinen. H. O.: A new table of binary-ternary mixed covering codes. Designs, Codes Cryptography (submitted)
219. Pach, J., Spencer, J.: Explicit codes with low covering radius. IEEE Trans. Inform. Theory 34, 1281-1285 (September 1988)
220. Panchenko, V. I.: Packings and coverings over an arbitrary alphabet. Problemy Peredachi Informatsii 24, 93-96 (1988). Translated in: Problems Inform. Transmission 24(4), 331-333 (1988)
221. Panchenko, V. I.: Packings and coverings over an arbitrary alphabet. Problemy Peredachi Informatsii 24, 93-96 (1988). Translated in: Problems Inform. Transmission 24(4), 331-333 (1988)
222. 15, 16)Reed-Muller code is at least 16276. IEEE Trans. Inform. Theory 29, 354-356 (May 1983)
223. 1,.16) Reed-Muller code is at least 16276". IEEE Trans. Inform. Theory 36, 443 (March 1990)
224. Phelps, K. T.: A combinatorial construction of perfect codes. SIAM J. Algebraic Discrete Methods 4, 398-403 (1983)
225. Phelps, K. T.: A general product construction for error correcting codes. SIAM J. Algebraic Discrete Methods 5, 224-228 (1984)
226. Phelps, K. T.: Dual product constructions of Reed-Muller type codes. IEEE Trans. Inform. Theory 32, 103-106 (January 1986)
227. Reuvers, H. F. H.: Some non-existence theorems for perfect codes over arbitrary alphabets. Thesis, Eindhoven University of Technology, The Netherlands (1977)
228. Rivest, R. L., Shamir, A.: How to reuse a "write-once" memory. Inform, and Control 55, 1-19 (1982)
229. Rodemich, E. R.: Coverings by rook domains. J. Combinatorial Theory, Ser. A 9, 117-128 (1970)
230. Rödl, V.: On a packing and covering problem. Europ. J. Combinatorics 6, 69-78 (1985)
231. Rothaus, O.: On "bent" functions. J. Combinatorial Theory, Ser. A 20, 300-305 (1976)
232. Rush, J. A.: Thin lattice coverings. J. London Math. Soc. (2) 45, 193-200 (1992)
233. Schatz, J. R.: The second order Reed-Muller code of length 64 has covering radius 18. IEEE Trans. Inform. Theory 27, 529-530 (July 1981)
234. Schönheim, J.: Mixed codes. Proc. Calgary Internat. Conf. on Combinatorial Structures and their Applications, p. 385. New York: Gordon and Breach 1970
235. Shparlinski, I. E.: Computational and Algorithmic Problems in Finite Fields. Dordrecht: Kluwer 1992
236. Simonis, J.: The minimal covering radius t [15, 6] of a 6-dimensional binary linear code of length 15 is equal to 4. IEEE Trans. Inform. Theory 34, 1344-1345 (September 1988)
237. Simonis, J.: Covering radius: improving on the sphere-covering bound. Lecture Notes in Computer Science, vol. 357, pp. 377-385. Berlin, Heidelberg, New York: Springer 1989
238. Skorobogatov, A. N.: On the covering radius of BCH codes. Third Internat. Workshop on Information Theory, Abstracts of papers, pp. 308-309, Sochi (1987)
239. Skorobogatov, A. N.: The parameters of subcodes of algebraic-geometric codes over prime subfields. Discrete Appl. Math. 33, 205-214 (1991)
240. Sloane, N. J. A.: A new approach to the covering radius of codes. J. Combinatorial Theory, Ser. A 42, 61-86 (1986)
241. Sloane, N. J. A.: Unsolved problems related to the covering radius of codes. In: Open Problems in Communication and Computation, pp. 51-56. Berlin, Heidelberg, New York: Springer 1987
242. Sloane, N. J. A., Dick, R. J.: On the enumeration of cosets of first order Reed-Muller codes Proc. IEEE Internat. Conf. Communications 7, 362-366 (1971)
243. Sloane, N. J. A., Reddy, S. M., Chen, C. L.: New binary codes. IEEE Trans. Inform. Theory 18, 503-510(July 1972)
244. Solé, P.: Rayon de recouvrement et schémas d'association. Thèse, Télécom Paris, France, 66 (1987)
245. Solé, P.: Asymptotic bounds on the covering radius of binary codes. IEEE Trans. Inform. Theory 36, 1470-1472 (November 1990)
246. Solé P.: Covering codes and combinatorial optimization. Lecture Notes in Computer Science, vol. 539, pp. 426-433. Berlin, Heidelberg, New York: Springer 1991
247. Solé, P.. Mehrotra, K. G.: Generalization of the Norse bounds to codes of higher strength. IEEE Trans. Inform. Theory 37, 190-192 (January 1991)
248. Solé, P., Stokes, Ph.: Covering radius, codimension and dual-distance width. IEEE Trans. Inform. Theory 39, 1195-1203 (July 1993).
249. Solé, P., Zaslavsky, T.: The covering radius of the cycle code of a graph. Discrete Appl. Math. 45, 63-70 (1993)
250. Stanton, R.G.: Covering theorems in groups (or: how to win at football pools). In: Recent Progress in Combinatorics, pp. 21-36. New York: Academic Press 1969
251. Stanton, R. G., Horton, J. D., Kalbfleisch. J. G.: Covering theorems for vectors with special reference to the case of four and five components. J. London Math. Soc. 1, 493-499 (1969)
252. Stanton, R. G., Kalbfleisch, J. G.: Covering problems for dichotomized matchings. Aequationes Math. 1, 94-103 (1968)
253. Stanton R. G., Kalbfleisch, J. G.: Intersection inequalities for the covering problem. SIAM J. Appl. Math. 17, 1311-1316 (1969)
254. Struik, R.: Constructive non-existence proofs for covering codes. Presented at Oberwolfach Workshop on Inform. Theory, April 1992
255. Struik. R.: Constructive non-existence proofs for linear covering codes. IEEE Symposium on Inform. Theory, Abstracts of papers, p. 369, San Antonio, January 1993
256. Struik, R.: An improvement of the van Wee bound for binary linear covering codes. IEEE Trans. Inform. Theory 40, 1280-1284 (July 1994)
257. Struik, R.: On the structure of linear codes with covering radius two and three. IEEE Trans. Inform. Theory 40, 1406-1416 (September 1994)
258. Struik, R.: Covering codes. Ph.D. Thesis, Eindhoven University of Technology, The Netherlands, 106 p. (1994)
259. Taussky, O., Todd. J.: Covering theorems for groups. Annales Soc. Polonaise Math. 21, 303-305 (1948).
260. Tietäväinen, A.: On the covering radius of long binary BCH codes. Discrete Appl. Math. 16, 75-77 (1987)
261. Tietäväinen, A.: Codes and character sums. Lecture Notes in Computer Science, vol. 388, pp. 3-12. Berlin, Heidelberg, New York: Springer 1989
262. Tietäväinen, A.: An asymptotic bound on the covering radii of binary BCH codes. IEEE Trans. Inform. Theory 36, 211-213 (January 1990)
263. Tietäväinen, A.: An upper bound on the covering radius as a function of the dual distance. IEEE Trans. Inform. Theory 36, 1472-1474 (November 1990)
264. Tietäväinen, A.: Covering radius and dual distance. Designs. Codes Cryptography 1(1), 31-46 (May 1991)
265. van Tilborg, H. C. A.: On the uniqueness (resp. nonexistence) of certain codes meeting the Griesmer bound. Inform, and Control 44, 16-35 (1980)
266. Tsfasman, M., Vleduts, S. G.: Algebraic-geometric codes. Boston: Kluwer 1991
267. 3(n, d). Discrete Appl. Math. 45, 71-87 (1993)
268. Velikova, E.: Bounds on the covering radius of linear codes. Comptes-Rendus Académie Bulgare Sciences, 41, 13-16 (1988)
269. Velikova, E.: Covering radius of some cyclic codes. Internat. Workshop on Algebraic and Combinatorial Coding Theory, Abstracts of papers, pp. 165-169, Varna (1988)
270. Vleduts, S. G., Skorobogatov, A. N.: Covering radius for long BCH codes. Problemy Peredachi Informatsii 25, 38-45 (1989). Translated in: Problems Inform. Transmission 25(1), 28-34 (1989)
271. Vleduts, S. G., Skorobogatov, A. N.: Covering radius for long BCH codes. Problemy Peredachi Informatsii 25, 38-45 (1989). Translated in: Problems Inform. Transmission 25(1), 28-34 (1989)
272. Weber, E. W.: On the football pool problem for 6 matches: a new upper bound. J. Combinatorial Theory, Ser. A 35, 106-108 (1983)
273. van Wee, G. J. M.: Improved sphere bounds on the covering radius of codes. IEEE Trans. Inform. Theory 34, 237-245 (March 1988)
274. van Wee, G. J. M.: More binary covering codes are normal. IEEE Trans. Inform. Theory 36, 1466-1470 (November 1990)
275. van Wee, G. J. M.: On the non-existence of certain perfect mixed codes. Discrete Mathematics 87, 323-326 (1991)
276. van Wee, G. J. M.: Bounds on packing and coverings by spheres in q-ary and mixed Hamming spaces. J. Combinatorial Theory, Ser. A 57, 117-129 (1991)
277. van Wee, G. J. M.: Some new lower bounds for binary and ternary covering codes. IEEE Trans. Inform. Theory 39, 1422-1424 (July 1993)
278. van Wee, G. J. M., Cohen, G. D., Litsyn, S. N.: A note on perfect multiple coverings of the Hamming space. IEEE Trans. Inform. Theory 37, 678-682 (May 1991)
279. Wille, L. T.: The football pool problem for 6 matches: a new upper bound obtained by simulated annealing. J. Combinatorial Theory, Ser. A 45, 171-177 (1987)
280. Wille, L. T.: Personal communication (1987)
281. Wille, L. T.: Improved binary code coverings by simulated annealing. Congressus Numerantium 73, 53-58 (1990)
282. Ytrehus, Ø.: Binary [18, 11]2 codes do not exist - nor do [64, 53]2 codes. IEEE Trans. Inform. Theory 37, 349-351 (March 1991)
283. Zaremba, S. K.: A covering theorem for abelian groups. J. London Math. Soc. 26, 71-72 (1950)
284. Zaremba, S. K.: Covering problems concerning abelian groups. J. London Math. Soc. 27, 242-246 (1952)
285. Zelinka, B.: Domatic numbers of cube graphs. Math. Slovaca 32, 117-119 (1982)
286. Zémor, G.: Problèmes combinatoires liés à l'écriture sur des mémoires. Thèse, Télécom Paris, France, 109 p. (1989)
287. Zémor, G., Cohen, G. D.: Error-correcting WOM-codes. IEEE Trans. Inform. Theory 37, 730-734 (May 1991)
288. Zhang, Z.: Linear inequalities for covering codes: Part I - pair covering inequalities. IEEE Trans. Inform. Theory 37, 573-582 (May 1991)
289. Zhang, Z., Lo, C.: Linear inequalities for covering codes: Part II - triple covering inequalities. IEEE Trans. Inform. Theory 38, 1648-1662 (November 1992)
290. Zhang, Z., Lo. C.: Lower bounds on r[n, k] from linear inequalities. IEEE Trans. Inform. Theory 38, 194-197 (January 1992)