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

09/11/2018

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by   Saban Alaca, et al.

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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 F_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.