Finite fields
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Abelian Difference Sets Without Self-conjugacy
Designs, Codes and Cryptography
On non-existence of perfect and nearly perfect sequences
International Journal of Information and Coding Theory
Sequences and functions derived from projective planes and their difference sets
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
Nonexistence of certain almost p-ary perfect sequences
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
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A sequence a = (a0, a1, a2, ..., an) is said to be an almost p-ary sequence of period n + 1 if a0 = 0 and ai = ξpbi for 1 ≤ i ≤ n, where ξp is a primitive p-th root of unity and bi ∈ {0, 1, ..., p - 1}. Such a sequence a is called perfect if all its out-of-phase autocorrelation coefficients are zero; and is called nearly perfect if its out-of-phase auto-correlation coefficients are all 1, or are all -1. In this paper, on the one hand, we construct almost p-ary perfect and nearly perfect sequences; on the other hand, we present results to show they do not exist with certain periods. It is shown that almost p-ary perfect sequences correspond to certain relative difference sets, and almost p-ary nearly perfect sequences correspond to certain direct product difference sets. Finally, two tables of the existence status of such sequences with period less than 100 are given.