The Constructions of Optimal Balanced Quadriphase Almost Mismatched Complementary Pairs with Prime Length

A pair of mismatched sequences is called an almost mismatched complementary pair if their periodic autocorrelation functions sum up to a same nonzero integer for all out-of-phase time shifts. In this paper, a new balanced quadriphase almost mismatched complementary pair is proposed, the theoretical bound of balanced quadriphase almost complementary pair with prime length is proved by Gray mapping, based on the cyclotomic classes of order 4, the optimal balanced quadriphase almost mismatched complementary pair with prime length satisfied theoretical bound is constructed. The existence of quadriphase complementary pairs are expanded and compensated the deficiency of most of the existing ones only have even length at present by investigate in this paper.