Row-correlation function: A new approach to complementary code matrices

摘要

New tools are developed for testing Complementary Code Matrix (CCM) existence, first for binary CCMs and then for more general p-phase classes, by formulating a CCM in terms of its row-correlation function. It is shown that a result of Lam and Leung on vanishing sums of roots of unity is useful in this approach for developing p-phase CCM existence tests in terms of the prime factorization of p. In addition, other existence tests and properties are found by using the row-correlation function to derive new dot product and congruence relations between rows of a CCM.