On the complete weight enumerators of some reducible cyclic codes

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,^g2εFr∗. 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=β^g1, where h>1 is a divisor of q-1, e>1 is a divisor of h, and β=θr-^1e; (2) ^g1=^θ2,^g2=θ^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.