Complete Mutually Orthogonal Golay Complementary Sets From Reed–Muller Codes

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 RM 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.