Perfect and almost perfect sequences

Discrete Applied Mathematics

Volumn 95, Issue 1-3, 1999, Pages 331-359

  Jungnickel, Dieter ^a   Pott, Alexander ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

Almost perfect sequence; Autocorrelation function; Barker sequence; Binary sequence; Difference set; Merit factor; Perfect sequence; Periodic sequence; Relative difference set

Indexed keywords

EID: 0038537970     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(99)00085-2     Document Type: Article

References (84)

1. K.T. Arasu, J.A. Davis, J. Jedwab, S. Sehgal, New constructions of Menon difference sets, J. Combin. Theory Ser. A 64 (1993) 329-336.
2. K.T. Arasu, J.F. Dillon, D. Jungnickel, A. Pott, The solution of the Waterloo problem, J. Combin. Theory Ser. A 71 (1995) 316-331.
3. K.T. Arasu, D. Jungnickel, S.L. Ma, A. Pott, Relative difference sets with n=2, Discrete Math. 147 (1995) 1-17.
4. ⊥ = 1, Discrete Math. 97 (1991) 25-38.
5. K.T. Arasu, D. Jungnickel, A. Pott, The Mann test for divisible difference sets, Graphs Combin. 7 (1991) 209-217.
6. K.T. Arasu, S.L. Ma, N.J. Voss, On a class of almost perfect sequences, J. Algebra 192 (1997) 47-56.
7. K.T. Arasu, Q. Xiang, Multiplier theorems, J. Combin. Designs 3 (1995) 257-267.
8. R.H. Barker, Group synchronizing of binary digital systems, in: W. Jackson (Ed.), Communication Theory Butterworths, London, 1953.
9. T. Beth, D. Jungnickel, H. Lenz, Design Theory, second ed., Cambridge University Press, Cambridge, 1999.
10. R.C. Bose, W.S. Connor, Combinatorial properties of group divisible designs, Ann. Math. Statist. 23 (1952) 367-383.
11. S.P. Bradley, A. Pott, Existence and nonexistence of almost-perfect autocorrelation sequences, IEEE Trans. Inform. Theory 41 (1995) 301-304.
12. W.J. Broughton, A note on Table 1 of "Barker sequences and difference set", L'Enseignement Math. 50 (1995) 105-107.
13. D. Calabro, J.K. Wolf, On the synthesis of two-dimensional arrays with desirable correlation properties, Inform, and Control 11 (1968) 537-560.
14. W.G. Chambers, Basics of Communication and Coding, Clarendon Press, Oxford, 1985.
15. W.K. Chan, M.K. Siu, Summary of perfect s × t-arrays, 1 ≤s≤t≤100, Electron. Lett. 27 (1991) 709-710.
16. W.K. Chan, M.K. Siu, Correction to Summary of perfect s × t-arrays, 1≤s≤t≤100, Electron. Lett. 27 (1991) 1112.
17. W.K. Chan, M.K. Siu, P. Tong, Two-dimensional binary array with good autocorrelation, Inform, and Control 42 (1979) 125-130.
18. Y.Q. Chen, On the existence of abelian Hadamard difference sets and a new family of difference sets, Finite Fields Appl. 3 (1997) 234-256.
19. J.A. Davis, J. Jedwab, A survey of Hadamard difference sets, in: K.T. Arasu, J.F. Dillon, K. Harada, S.K. Sehgal, R. Solomon (Eds.), Groups, Difference sets and the Monster deGruyter, Berlin, 1996, pp. 145-156.
20. J.A. Davis, K. Smith, A construction of difference sets in high exponent 2-groups using representation theory, J. Alg. Combin. 3 (1994) 137-151.
21. P. Delsarte, J.M. Goethals, J.J. Seidel, Orthogonal matrices with zero diagonal II, Canad. J. Math. 23 (1971) 816-832.
22. R.H. Dicke, Scatter-hole cameras for X-rays and γ-rays, Astrophys. J. 153 (1968) L101-L106.
23. J.F. Dillon, Multiplicative difference sets via additive characters, Designs Codes Cryptogr., to appear.
24. J.F. Dillon, H. Dobbertin, Cyclic difference sets with Singer parameters, manuscript.
25. S. Eliahou, M. Kervaire, Barker sequences and difference sets, L'Enseignement Math. 38 (1992) 345-382.
26. S. Eliahou, M. Kervaire, B. Saffari, A new restriction on the length of Golay complementary sequences, J. Combin. Theory (A) 55 (1990) 45-59.
27. R. Evans, H. Hollmann, C. Krattenthaler, Q. Xiang, Gauss sums, Jacobi sums, and p-ranks of cyclic difference sets, J. Combin. Theory (A), to appear.
28. E.E. Fenimore, Coded aperture imaging: predicted performance of uniformly redundant arrays, Appl. Opt. 17 (1978) 3562-3570.
29. E.E. Fenimore, T.M. Cannon, Coded aperture imaging with uniformly redundant arrays, Appl. Opt. 17 (1978) 337-347.
30. P. Gaal, S.W. Golomb, Exhaustive determination of (1023, 511, 255)-cyclic difference sets, preprint.
31. R.A. Games, The geometry of quadrics and correlations of sequences, IEEE Trans. Inform. Theory 32 (1986) 423-426.
32. A. Gavish, A. Lempel, On ternary complementary sequences, IEEE Trans. Inform. Theory 40 (1994) 522-526.
33. M.J.E. Golay, Sieves for low autocorrelation binary sequences, IEEE Trans. Inform. Theory 23 (1977) 43-51.
34. S.W. Golomb, Shift register sequences, Aegean Park Press, Laguna Hills, CA, 1982.
35. B. Gordon, W.H. Mills, L.R. Welch, Some new difference sets, Canad. J. Math. 14 (1962) 614-625.
36. S.R. Gottesman, E.E. Fenimore, New family of binary arrays for coded aperture imaging, Appl. Opt. 28 (1989) 4344-4352.
37. S.R. Gottesman, E.J. Schneid, PNP - a new class of binary coded aperture arrays, IEEE Trans. Nuclear Sci. 33 (1986) 745-749.
38. A.R. Gourley, J.B. Stephen, Geometric coded aperture masks, Appl. Opt. 22 (1983) 4042-4047.
39. C. de Groot, D. Würtz, K.H. Hoffmann, Low autocorrelation binary sequences: exact enumeration and optimization by evolutionary strategies, Optimization 23 (1991) 369-384.
40. T. Hoholdt, J. Justesen, Ternary sequences with perfect periodic autocorrelation, IEEE Trans. Inform. Theory 29 (1983) 597-600.
41. V.P. Ipatov, Ternary sequences with ideal periodic autocorrelation properties, Radio Eng. Electron Phys. 24 (1979) 75-79.
42. J. Jedwab, Nonexistence of perfect binary arrays, Electron. Lett. 27 (1991) 1252-1254.
43. J. Jedwab, Nonexistence of certain perfect binary arrays, Electron. Lett. 29 (1993) 99-101.
44. J.M. Jensen, H.E. Jensen, T. Hoholdt, The merit factor of binary sequences related to difference sets, IEEE Trans. Inform. Theory 37 (1991) 617-626.
45. D. Jungnickel, On automorphism groups of divisible designs, Canad. J. Math. 34 (1982) 257-297.
46. D. Jungnickel, On a theorem of Ganley, Graphs Combin. 3 (1987) 141-143.
47. D. Jungnickel, On affine difference sets, Sankhyā 54 (1987) 219-240.
48. D. Jungnickel, A. Pott, Computational nonexistence results for abelian affine difference sets, Congr. Numer. 68 (1989) 91-98.
49. D. Jungnickel, V.D. Tonchev, Decompositions of difference sets, J. Algebra, to appear.
50. L.E. Kopilovich, On perfect binary arrays, Electron. Lett. 24 (1988) 566-567.
51. L.E. Kopilovich, New approach to constructing two-dimensional aperture synthesis systems, IEE Proc.-F 139 (1992) 365-368.
52. L.E. Kopilovich, L.G. Sodin, Two-dimensional aperiodic antenna arrays with a low sidelobe level, IEE Proc.-H 138 (1991) 233-237.
53. L.E. Kopilovich, L.G. Sodin, Synthesis of coded masks for gamma-ray and X-ray telescopes, Mon. Not. R. Astron. Soc. 266 (1994) 357-359.
54. R.G. Kraemer, Proof of a conjecture on Hadamard 2-groups, J. Combin. Theory (A) 63 (1993) 1-10.
55. P.V. Kumar, Frequency-hopping code sequence designs having large linear span, IEEE Trans. Inform. Theory 34 (1988) 146-151.
56. P.V. Kumar, On the existence of square dot-matrix patterns having a specific three-valued periodic-correlation funtion, IEEE Trans. Inform. Theory 34 (1988) 271-277.
57. E.S. Lander, Symmetric Designs: An Algebraic Approach, London Math. Soc. Lecture Notes, vol. 75, Cambridge University Press, Cambridge, 1983.
58. P. Langevin, Almost perfect binary functions, App. Alg. Eng. Comm. Comp. 4 (1993) 95-102.
59. A. Lempel, M. Cohn, W. Eastman, A class of balanced binary sequences with optimal autocorrelation properties, IEEE Trans. Inform. Theory 23 (1977) 38-42.
60. K.H. Leung, S. Ling, S.L. Ma, K.B. Tay, Almost perfect sequences with θ=2, Arch. Math. 70 (1998) 128-131.
61. H.D. Lüke, Sequences and arrays with perfect periodic correlation, IEEE Trans. Aerospace Electron. Syst. 27 (1988) 287-294.
62. H.D. Lüke, Korrelationssignale, Springer, Berlin, 1992.
63. S.L. Ma, A survey on partial difference sets, Designs Codes Cryptogra. 4 (1994) 221-261.
64. F.J. MacWilliams, N.J.A. Sloane, Pseudo-random sequences and arrays, Proc. IEEE 64 (1976) 1715-1729.
65. H.B. Mann, Addition theorems, Wiley, New York, 1965.
66. A. Maschietti, Difference sets and hyperovals, Designs Codes Cryptogra. 14 (1998) 89-98.
67. S. Mertens, Exhaustive search for low-autocorrelation binary sequences, J. Phys. A 29 (1996) 473-481.
68. S. Mertens, C. Bessenrodt, On the ground states of the Bernasconi model, submitted for publication.
69. n - 1 with ideal autocorrelation, IEEE Trans. Inform. Theory 44 (1998) 814-817.
70. A. Pott, Finite Geometry and Character Theory, Lecture Notes in Mathematics, vol. 1601, Springer, Berlin, 1995.
71. D. Reuschling, Zur Existenz von ω-zirkulanten Konferenz-Matrizen, Diplomarbeit, Universität Augsburg, 1994.
72. D.V. Sarwate, M.B. Pursley, Crosscorrelation properties of pseudorandom and related sequences, Proc. IEEE 68 (1980) 593-619.
73. B. Schmidt, Differenzmengen und relative Differenzmengen, Augsburger Mathematisch-Naturwissenschaftliche Schriften Band 4, Augsburg, 1995.
74. B. Schmidt, Cyclotomic integers and finite geometry, J. Amer. Math. Soc., to appear.
75. R.A. Scholtz, L.R. Welch, GMW sequences, IEEE Trans. Inform. Theory 30 (1984) 548-553.
76. M.R. Schroeder, Binaural dissimilarity and optimum ceilings for concert halls: More lateral sound diffusion, J. Acoust. Soc. 65 (1979) 958-963.
77. M.R. Schroeder, Number theory in science and communication, Springer, New York, 1986.
78. H.Y. Song, S.W. Golomb, On the existence of cyclic Hadamard difference sets, IEEE Trans. Inform. Theory 40 (1994) 1266-1268.
79. R.J. Turyn, Characer sums and difference sets, Pacific J. Math. 15 (1965) 319-346.
80. R.J. Turyn, A special class of Williamson matrices and difference sets, J. Combin. Theory Ser. A 36 (1984) 111-115.
81. R.J. Turyn, J. Storer, On binary sequences, Proc. Amer. Math. Soc. 12 (1961) 394-399.
82. G. Wilhelmi, F. Gompf, Binary sequences and error analysis for pseudo-statistical neutron modulators with different duty cycles, Nucl. Instr. Meth. 81 (1970) 36-44.
83. J. Wolfman, Almost perfect autocorrelation sequences, IEEE Trans. Inform. Theory 38 (1992) 1412-1418.
84. M. Xia, Some infinite classes of special Williamson matrices and difference sets, J. Combin. Theory Ser. A 61 (1992) 230-242.