On the number of Z2Z4 and ZpZp2-additive cyclic codes

Abstract

In this paper, we give the exact number of Z(2)Z(4)-additive cyclic codes of length n = r + s, for any positive integer r and any positive odd integer s. We will provide a formula for the the number of separable Z(2)Z(4)-additive cyclic codes of length n and then a formula for the number of non-separable Z(2)Z(4)-additive cyclic codes of length n. Then, we have generalized our approach to give the exact number of Z(p)Z(p2)-additive cyclic codes of length n = r + s, for any prime p, any positive integer r and any positive integer s where gcd (p, s) = 1. Moreover, we will provide examples of the number of these codes with different lengths n = r + s.