Complete Mutually Orthogonal Golay Complementary Sets From Reed–Muller Codes

摘要

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.