Shift-Inequivalent Decimations of the Sidelnikov-Lempel-Cohn-Eastman Sequences

2018/09/11 by Şaban Alaca, Saban Alaca, Alaca, Saban +2 · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #cs.IT #math.CO #math.IT #math.NT

paper · pdf · doi:10.48550/arxiv.1809.04010

arxiv created 2018/09/11 · arxiv updated 2018/09/12

Abstract

We consider the problem of finding maximal sets of shift-inequivalent decimations of Sidelnikov-Lempel-Cohn-Eastman (SLCE) sequences (as well as the equivalent problem of determining the multiplier groups of the almost difference sets associated with these sequences). We derive a numerical necessary condition for a residue to be a multiplier of an SLCE almost difference set. Using our necessary condition, we show that if p is an odd prime and S is an SLCE almost difference set over \mathbbF_p, then the multiplier group of S is trivial. Consequently, for each odd prime p, we obtain a family of ϕ(p-1) shift-inequivalent balanced periodic sequences (where ϕ is the Euler-Totient function) each having period p-1 and nearly perfect autocorrelation.

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