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## Abstract Binary Golay sequence pairs exist for lengths 2, 10 and 26 and, by Turyn's product construction, for all lengths of the form 2^__a__^10^__b__^26^__c__^ where __a, b, c__ are non‐negative integers. Computer search has shown that all inequivalent binary Golay sequence pairs of length less than 100 can be constructed from five “seed” pairs, of length 2, 10, 10, 20 and 26. We give the first complete explanation of the origin of the length 26 binary Golay seed pair, involving a Barker sequence of length 13 and a related Barker sequence of length 11. This is the special case __m__=1 of a general construction for a length 16__m__+10 binary Golay pair from a related pair of Barker sequences of length 8__m__+5 and 8__m__+3, for integer __m__≥0. In the case __m__=0, we obtain an alternative explanation of the origin of one of the length 10 binary Golay seed pairs. The construction cannot produce binary Golay sequence pairs for __m__>1, having length greater than 26, because there are no Barker sequences of odd length greater than 13. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 478–491, 2009

Author

Jonathan Jedwab; Matthew G. Parker

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 1063-8539)

Published

2009

Language

EN