A class of p-ary cyclic codes and their weight enumerators

Let m, k be positive integers such that m gcd(m,k) ≥ 3, p be an odd prime and π be a primitive element of Fpm. Let h1(x) and h2(x) be the minimal polynomials of −π−1 and π pk+1 2 over Fp, respectively. In the case of odd m gcd(m,k) , when k is even, gcd(m,k) is odd or when k gcd(m,k) is odd, Zhou et al. in [25] obtained the weight distribution of a class of cyclic codes C over Fp with parity-check polynomial h1(x)h2(x). In this paper, we further investigate this class of cyclic codes C over Fp in the rest case of odd m gcd(m,k) and the case of even m gcd(m,k) . Moreover, we determine the weight distribution of cyclic codes C.