Quaternary Golay sequence pairs I: even length

Authors:
Richard G. Gibson;Jonathan Jedwab
Affiliations:
Department of Computing Science, University of Alberta, Edmonton, Canada T6G 2E8;Department of Mathematics, Simon Fraser University, Burnaby, Canada V5A 1S6
Venue:
Designs, Codes and Cryptography
Year:
2011

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Abstract

The origin of all 4-phase Golay sequences and Golay sequence pairs of even length at most 26 is explained. The principal techniques are the three-stage construction of Fiedler, Jedwab and Parker involving multi-dimensional Golay arrays, and a "sum---difference" construction that modifies a result due to Eliahou, Kervaire and Saffari. The existence of 4-phase seed pairs of lengths 3, 5, 11, and 13 is assumed; their origin is considered in (Gibson and Jedwab, Des Codes Cryptogr, 2010).