Quaternary Golay sequence pairs Ⅱ:odd length

摘要

A 4-phase Golay sequence pair of length s≡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≡5 (mod 8).