Almost supplementary difference sets and quaternary sequences

2019/11/20 by Armario, J. A., Flannery, D. L.
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.08828

Abstract

We introduce almost supplementary difference sets (ASDS). For odd m, certain ASDS in \mathbb Z_m that have amicable incidence matrices are equivalent to quaternary sequences of odd length m with optimal autocorrelation. As one consequence, if 2m-1 is a prime power, or m ≡ 1 \mod 4 is prime, then ASDS of this kind exist. We also explore connections to optimal binary sequences and group cohomology.

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