WEIGHT DISTRIBUTIONS OF A CLASS OF CYCLIC CODES FROM F-l-CONJUGATES

Abstract

Let F-qk be a finite field and a a primitive element of F-qk, where q = l(f), l is a prime power, and f is a positive integer. Suppose that N is a positive integer and m(glu) (x) is the minimal polynomial of g(lu) over F-q for u = 0, 1, ..., f - 1, where g = alpha(-N). Let C be a cyclic code over F-q with check polynomial m(g)(x)m(gl) (x) ... m(glf-1) (x). In this paper, we shall present a method to determine the weight distribution of the cyclic code C in two cases: (1) gcd(q(k)-1/l-1, N) = 1; (2) l = 2 and f = 2. Moreover, we will obtain a class of two-weight cyclic codes and a class of new three-weight cyclic codes.