Complete Mutually Orthogonal Golay Complementary Sets From Reed–Muller Codes

Abstract

Recently Golay complementary sets were shown to exist in the subsets of second-order cosets of a 𝑞-ary generalization of the first-order Reed–Muller (RM) code. We show that mutually orthogonal Golay complementary sets can also be directly constructed from second-order cosets of a 𝑞-ary generalization of the first-order <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RM</i> code. This identification can be used to construct zero correlation zone (ZCZ) sequences directly and it also enables the construction of ZCZ sequences with special subsets.