Complementary series

Golay, M.

doi:10.1109/tit.1961.1057620

Cited by 1,312 publications

(702 citation statements)

References 2 publications

Supporting

Mentioning

674

Contrasting

Unclassified

Order By: Relevance

“…Golay sequences GS(n) exist for n = 2 a Io"26 c (Golay numbers) where a, b, c are nonnegative integers [5], [7], [8], [18].…”

Section: A(z)a(z-') + B(z)b(z-')mentioning

confidence: 99%

“…) = 4n + 2p, z i= 0 (7) where A(z), B(z), C(z), D(z) are the associated polynomials. Base sequences of lengths n + 1. n + I, n, n are denoted by BS(2n + 1).…”

Section: A (Z)a(z-') + B(z)b(z~') + C(z)c(z-') + D(z)d(z-mentioning

confidence: 99%

“…Base sequences of lengths n + 1. n + I, n, n are denoted by BS(2n + 1). From (7) and for p = I, if we set z = 1 we obtain (8) where TS(2n + 1) exist for n ~ 7, n = 12,14. They cannot exist for n = 10,11,16,17 and for n = 8,9, 13, 15, TS(2n + 1) might exist but an exhaustive machine search showed that they do not exist (see [1], [6, pp.…”

Section: A (Z)a(z-') + B(z)b(z~') + C(z)c(z-') + D(z)d(z-mentioning

confidence: 99%

“…Base, Turyn, Golay and nonnal sequences are finite sequences, with zero autocorrelation function, useful in constructing orthogonal designs and Hadamard matrices [6], in communications engineering [18], in optics and signal transmission problems [7], [11], etc.…”

Section: Introductionmentioning

confidence: 99%

“…See [5], [6], [7]. From this definition and relation (2) we conclude that two (1, -1) sequences of length n are GS(n) if and only if…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On sequences with zero autocorrelation

et al. 1994

View full text Add to dashboard Cite

Normal sequences of lengths n = 18, 19 are constructed. It is proved through an exhaustive search that normal sequences do not exist for n = 17,21,22,23. Marc Gysin has shown that normal sequences do not exist for n = 24. So the first unsettled case is n = 27. Base sequences of lengths 2n -1, 2n -1. n. n are constructed for all decompositions of 6n -2 into four squares for n = 2.4.6 ..... 20 and some base sequences for n = 22.24 are also given. So T-sequences (T-matrices) of length 71 are constructed here for the first time. This gives new Hadamard matrices of orders 213, 781, 1349, 1491, 1633, 2059, 2627, 2769, 3479, 3763, 4331, 4899, 5467, 5609, 5893, 6177, 6461,6603, 6887, 7739, 8023, 8591, 9159, 9443, 9727, 9869. Disciplines Physical Sciences and Mathematics Publication DetailsChristos Koukouvinos, Stratis Kounias, Jennifer Seberry, C. H. Yang, Joel Yang, On sequences with zero autocorrelation, Designs, Codes and Cryptography, 4, (1994), 327-340. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1090 Designs, Codes and Cryptography, 4, 327-340 (1994 Base sequences of lengths 2n -I. 2n -I. n. n are constructed for all decompositions of 6n -2 into four squares for n = 2.4.6 ..... 20 and some base sequences for n = 22.24 are also given. So T-sequences (T-matrices) of length 71 are constructed here for the first time. This gives new Hadamard matrices of orders 213.) © 1994 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. On Sequences with Zero Autocorrelation

show abstract

“…Golay sequences GS(n) exist for n = 2 a Io"26 c (Golay numbers) where a, b, c are nonnegative integers [5], [7], [8], [18].…”

Section: A(z)a(z-') + B(z)b(z-')mentioning

confidence: 99%

“…) = 4n + 2p, z i= 0 (7) where A(z), B(z), C(z), D(z) are the associated polynomials. Base sequences of lengths n + 1. n + I, n, n are denoted by BS(2n + 1).…”

Section: A (Z)a(z-') + B(z)b(z~') + C(z)c(z-') + D(z)d(z-mentioning

confidence: 99%