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Some new periodic Golay pairs

Authors :
Djokovic, Dragomir Z.
Kotsireas, Ilias S.
Source :
Numerical Algorithms (2015) 69, issue 3, 523--530
Publication Year :
2013

Abstract

Periodic Golay pairs are a generalization of ordinary Golay pairs. They can be used to construct Hadamard matrices. A positive integer $v$ is a (periodic) Golay number if there exists a (periodic) Golay pair of length $v$. Taking into the account the results obtained in this note and an yet unpublished new result, there are only seven known periodic Golay numbers which are definitely not Golay numbers, namely 34,50,58,68,72,74,82.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.<br />Comment: 8 pages, updated version (uses some new facts). Accepted by Numerical Algorithms 2014

Subjects

Subjects :
Mathematics - Combinatorics
11B83

Details

Database :
arXiv
Journal :
Numerical Algorithms (2015) 69, issue 3, 523--530
Publication Type :
Report
Accession number :
edsarx.1310.5773
Document Type :
Working Paper
Full Text :
https://doi.org/10.1007/s11075-014-9910-4