On Golay sequences

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Abstract

Golay sequences are two binary (+1, -1) sequences with nonperiodic autocorrelation function zero. These sequences have a wide range of applications in constructing orthogonal designs and Hadamard matrices, in coding theory, in multislit spectrometry and in surface acoustic wave devices. In this paper we develop an algorithm for constructing such sequences. We prove that Golay sequences of length n = 2 · 72t do not exist and we give new proofs of some known results. In particular we show there are no Golay sequences of length 98. We conjecture that there are no Golay sequences of length 2 · q2t where q is not the sum of two integer squares. © 1991.

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Kounias, S., Koukouvinos, C., & Sotirakoglou, K. (1991). On Golay sequences. Discrete Mathematics, 92(1–3), 177–185. https://doi.org/10.1016/0012-365X(91)90279-B

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