Numerical Algorithms

, Volume 69, Issue 3, pp 523–530 | Cite as

Some new periodic Golay pairs

Original Paper

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if there exists a (periodic) Golay pair of length v. Taking into the account the results obtained in this note and yet unpublished new result (Ðoković and Kotsireas, in preparation), there are only seven known periodic Golay numbers which are definitely not Golay numbers, namely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.

Keywords

Periodic Golay pairs Hadamard matrices 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Pure Mathematics and Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  2. 2.Department of Physics & Computer ScienceWilfrid Laurier UniversityWaterlooCanada

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