Quaternary Golay sequence pairs II: odd 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

Citing 0
Cited 2

Quaternary Golay sequence pairs I: even length

Designs, Codes and Cryptography
Paraunitary generation/correlation of QAM complementary sequence pairs

Cryptography and Communications

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Abstract

A 4-phase Golay sequence pair of length s 驴 5 (mod 8) is constructed from a Barker sequence of the same length whose even-indexed elements are prescribed. This explains the origin of the 4-phase Golay seed pairs of length 5 and 13. The construction cannot produce new 4-phase Golay sequence pairs, because there are no Barker sequences of odd length greater than 13. A partial converse to the construction is given, under the assumption of additional structure on the 4-phase Golay sequence pair of length s 驴 5 (mod 8).