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.

中文翻译：

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具有最佳自相关的几乎补充差分集和四元序列

我们介绍了几乎补充的差异集（ASDS）。对于奇数m，\（\ mathbb Z_ {m} \）中具有友好入射矩阵的某些ASDS等于具有最佳自相关的奇数长度m的四元序列。作为一个结果，如果2个米-图1是一个素数幂，或米≡1个模4素数，则ASDS这种存在的。我们还探讨了与最佳二进制序列和群同调的关系。