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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Acknowledgements
The first author thanks Kristeen Cheng for reading the manuscript, and Víctor Álvarez for assistance with computations. This research was partially supported by project FQM-016 funded by JJAA (Spain).
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Armario, J.A., Flannery, D.L. Almost supplementary difference sets and quaternary sequences with optimal autocorrelation. Cryptogr. Commun. 12, 757–768 (2020). https://doi.org/10.1007/s12095-019-00418-x
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DOI: https://doi.org/10.1007/s12095-019-00418-x