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Almost supplementary difference sets and quaternary sequences with optimal autocorrelation. (English) Zbl 1443.05024
Summary: 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 \(m \equiv 1\) mod 4 is prime, then ASDS of this kind exist. We also explore connections to optimal binary sequences and group cohomology.
MSC:
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
94A55 Shift register sequences and sequences over finite alphabets in information and communication theory
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