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arXiv · 1910.05661

Three-phase Golay sequence and array triads

Aki Ayukawa Avis·Jonathan Jedwab
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Abstract

3-phase Golay sequence and array triads are a natural generalisation of 2-phase Golay sequence pairs, yet their study has until now been largely neglected. We present exhaustive search results for 3-phase Golay sequence triads for all lengths up to 24, showing that the existence pattern is much richer than that for 2-phase Golay sequence pairs. We give an elementary proof that there is no 3-phase Golay sequence triad whose length is congruent to 4 modulo 6. We give two construction methods for 3-phase Golay array triads, and show how to project 3-phase Golay array triads to lower-dimensional Golay triads. In this way we explain much of the existence pattern found by exhaustive search.

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Aki Ayukawa Avis, Jonathan Jedwab. 2019-10-12. Three-phase Golay sequence and array triads. https://arxiv.org/abs/1910.05661

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