On the complete weight enumerators of some reducible cyclic codes

Abstract

Let F-r be a finite field with r = q(m) elements and theta a primitive element of F-r. Suppose that h(1)(x) and h(2)(x) are the minimal polynomials over F-q of g(1)(-1) and g(2)(-1), respectively, where g(1), g(2) is an element of F-r*Let C be a reducible cyclic code over F-q with check polynomial h(1)(x)h(2)(x). In this paper, we investigate the complete weight enumerators of the cyclic codes C in the following two cases: (l)g(1) = theta(q-1/h),g(2) = beta g(1), where h > 1 is a divisor of q - 1, e > 1 is a divisor of h, and beta = theta(r-1/e); (2) g(1) = theta(2), g(2) = theta(Pk+1), where q = p is an odd prime and k is a positive integer. Moreover, we explicitly present the complete weight enumerators of some cyclic codes.