Bounds on codes over an alphabet of five elements

Discrete Mathematics

Volumn 240, Issue 1-3, 2001, Pages 13-19

  Bogdanova, Galina T ^a   Östergård, Patrie R J ^b  

^a BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

^b AALTO UNIVERSITY   (Finland)

Author keywords

Code construction; Error correcting code; q ary code

Indexed keywords

EID: 0035964604     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(00)00383-6     Document Type: Article

References (21)

1. E.F. Assmus, Jr., H.F. Mattson, Jr., On weights in quadratic-residue codes, Discrete Math. 3 (1972) 1-20.
2. G.T. Bogdanova, A.E. Brouwer, S.N. Kapralov, P.R.J. Östergård, Error-correcting codes over an alphabet of four elements, Des. Codes Cryptogr., to appear.
3. 5, IEEE Trans. Inform. Theory 43 (1997) 308-313.
4. A.E. Brouwer, Bounds on the size of linear codes, in: V.S. Pless, W.C. Huffman (Eds.), Handbook of Coding Theory, Elsevier, Amsterdam, 1998, pp. 295-461.
5. A.E. Brouwer, H.O. Hämäläinen, P.R.J. Östergård, N.J.A. Sloane, Bounds on mixed binary/ternary codes, IEEE Trans. Inform. Theory 44 (1998) 140-161.
6. A.E. Brouwer, J.B. Shearer, N.J.A. Sloane, W.D. Smith, A new table of constant weight codes, IEEE Trans. Inform. Theory 36 (1990) 1334-1380.
7. R.N. Daskalov, T.A. Gulliver, Bounds on minimum distance for linear codes over GF(5), Appl. Algebra Eng. Comm. Comput. 9 (1999) 547-558.
8. P. Delsarte, Bounds for unrestricted codes, by linear programming, Philips Res. Rep. 27 (1972) 47-64.
9. S. Furino, Y. Miao, J. Yin, Frames and Resolvable Designs: Uses, Constructions, and Existence, CRC Press, Boca Raton, 1996.
10. H.O. Hämäläinen, Two new binary codes with minimum distance three, IEEE Trans. Inform. Theory 34 (1988) 875.
11. R.W. Hamming, Error detecting and error correcting codes, Bell System Tech. J. 29 (1950) 147-160.
12. R. Hill, Optimal linear codes, in: C. Mitchell (Ed.), Cryptography and Coding II, Oxford University Press, Oxford, 1992, pp. 75-104.
13. G.A. Kabatyanskii, V.I. Panchenko, Unit sphere packings and coverings of the Hamming space, Probl. Peredach. Inform. 24(4) (1988) 3-16. (English translation in Probl. Inform. Trans. 24 (1988) 261-272) (in Russian).
14. G.A. Kabatyanskii, V.I. Panchenko, Unit sphere packings and coverings of the Hamming space, Probl. Peredach. Inform. 24(4) (1988) 3-16. (English translation in Probl. Inform. Trans. 24 (1988) 261-272) (in Russian).
15. M. Kaikkonen, Codes from affine permutation groups, Des. Codes Cryptogr. 15 (1998) 183-186.
16. J.G. Kalbfleisch, R.G. Stanton, J.D. Horton, On covering sets and error-correcting codes, J. Combin. Theory 11 (1971) 233-250.
17. P.R.J. Östergå rd, wclique.c [C program; online], available at 〈URL:http://www.tcs.hut.fi/~pat/ wclique.html〉.
18. P.R.J. Östergård, T. Baicheva, E. Kolev, Optimal binary one-error-correcting codes of length 10 have 72 codewords, IEEE Trans. Inform. Theory 45 (1999) 1229-1231.
19. P.R.J. Östergård, M.K. Kaikkonen, New single-error-correcting codes, IEEE Trans. Inform. Theory 42 (1996) 1261-1262.
20. N.V. Semakov, V.A. Zinov'ev, Equidistant q-ary codes with maximal distance and resolvable balanced incomplete block designs, Probl. Peredach. Inform. 4(2) (1968) 3-10 (in Russian).
21. 3(n, d), Discrete Appl. Math. 45 (1993) 71-87.