Mismatched Binary Periodic Complementary Pairs with Period 3q

Abstract

Two mismatched sequences are called a mismatched periodic complementary pair if the sum of their periodic correlation functions is a delta function. In this paper, we present two constructions to obtain mismatched binary periodic complementary pairs with period 3q, where q is a prime, by using new generalized cyclotomy. One construction is based on the order 1 – 2, and the other is based on order 2 – 2. It is shown that many periods for which binary periodic complementary pairs are not exist become admissible for our constructions.