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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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