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Zbl 0808.05021
Koukouvinos, C.; Kounias, S.; Seberry, Jennifer; Yang, C.H.; Yang, J.
On sequences with zero autocorrelation. (English)
[J] Des. Codes Cryptography 4, No.4, 327-340 (1994). ISSN 0925-1022; ISSN 1573-7586/e

Summary: 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 $n = 27$. \par Base sequences of lengths $2n-1, 2n-1, n, n$ are constructed for all decompositions of $6n-2$ into four squares for $n = 2, 4, 6,\dots, 20$ 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.

MSC 2000:: *05B20 (0,1)-matrices (combinatorics)
68R05 Combinatorics in connection with computer science
62H20 Statistical measures of associations

Keywords: Turyn sequences; Golay sequences; zero autocorrelation; autocorrelation function; normal sequences; base sequences; T-sequences; T-matrices; Hadamard matrices

Cited in: Zbl 0818.05023

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