Three-phase Golay sequence and array triads
Combinatorics
2019-10-15 v1
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.
Cite
@article{arxiv.1910.05661,
title = {Three-phase Golay sequence and array triads},
author = {Aki Ayukawa Avis and Jonathan Jedwab},
journal= {arXiv preprint arXiv:1910.05661},
year = {2019}
}
Comments
23 pages, 3 tables, 1 figure