Weight distributions of a class of cyclic codes from F_l-conjugates

Let (formula presented) be a finite field and α a primitive element of (formula presented), where (formula presented), l is a prime power, and f is a positive integer. Suppose that N is a positive integer and (formula presented) is the minimal polynomial of (formula presented) over (formula presented) for u = 0; 1; : : : ; f – 1, where g = α^–N. Let C be a cyclic code over (formula presented) with check polynomial (formula presented). In this paper, we shall present a method to determine the weight distribution of the cyclic code C in two cases: (formula presented). Moreover, we will obtain a class of two-weight cyclic codes and a class of new three-weight cyclic codes.