On the complete weight enumerators of some reducible cyclic codes

Abstract

Let Fr be a finite field with r=qm elements and θ a primitive element of Fr. Suppose that h1(x) and h2(x) are the minimal polynomials over Fq of g1−1 and g2−1, respectively, where g1,g2∈Fr∗. Let C be a reducible cyclic code over Fq with check polynomial h1(x)h2(x). In this paper, we investigate the complete weight enumerators of the cyclic codes C in the following two cases: (1) g1=θq−1h,g2=βg1, where h>1 is a divisor of q−1, e>1 is a divisor of h, and β=θr−1e; (2) g1=θ2,g2=θpk+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.