Abstract
We have obtained an equality which expresses the absolute value of the real part of autocorrelation values of a sequence over the quaternions as a fraction of the sums of the norms of its particular elements. Based on this result, we obtained a condition necessary for perfection of a sequence over the quaternions. This condition becomes necessary and sufficient for perfection when applied to a symmetric sequence. Our result also allows increasing efficiency of the exhaustive search for perfect sequences. During exhaustive search experiments, we have attained up to 6 times reduction in computer time required for completion of the exhaustive search for perfect sequences, in comparison with the traditional method involving direct calculation of autocorrelation values. While we focused our study mainly on sequences over the quaternions, all results are equally applicable for sequences over the complex numbers.
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Kuznetsov, O. (2014). A Method of Optimisation of the Exhaustive Computer Search for Perfect Sequences. In: Schmidt, KU., Winterhof, A. (eds) Sequences and Their Applications - SETA 2014. SETA 2014. Lecture Notes in Computer Science(), vol 8865. Springer, Cham. https://doi.org/10.1007/978-3-319-12325-7_7
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DOI: https://doi.org/10.1007/978-3-319-12325-7_7
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