Some new periodic Golay pairs
Combinatorics
2015-08-05 v2
Abstract
Periodic Golay pairs are a generalization of ordinary Golay pairs. They can be used to construct Hadamard matrices. A positive integer is a (periodic) Golay number if there exists a (periodic) Golay pair of length . Taking into the account the results obtained in this note and an yet unpublished new result, there are only seven known periodic Golay numbers which are definitely not Golay numbers, namely 34,50,58,68,72,74,82. We construct here periodic Golay pairs of lengths 74,122,164,202,226. It is apparently unknown whether 122,164,202,226 are Golay numbers. The smallest length for which the existence of periodic Golay pairs is undecided is now 90.
Cite
@article{arxiv.1310.5773,
title = {Some new periodic Golay pairs},
author = {Dragomir Z. Djokovic and Ilias S. Kotsireas},
journal= {arXiv preprint arXiv:1310.5773},
year = {2015}
}
Comments
8 pages, updated version (uses some new facts). Accepted by Numerical Algorithms 2014