The weight distributions of two classes of p-ary cyclic codes

Let p be an odd prime, and m, k   be positive integers with m≥3km≥3k. Let C1C1 and C2C2 be cyclic codes over FpFp with parity-check polynomials h2(x)h3(x)h2(x)h3(x) and h1(x)h2(x)h3(x)h1(x)h2(x)h3(x), respectively, where h1(x)h1(x), h2(x)h2(x) and h3(x)h3(x) are the minimal polynomials of γ−1γ−1, γ−(pk+1)γ−(pk+1) and γ−(p3k+1)γ−(p3k+1) over FpFp, respectively, for a primitive element γ   of FpmFpm. Recently, Zeng et al. (2010) obtained the weight distribution of C2C2 for mgcd(m,k) being odd. In this paper, we determine the weight distribution of C1C1, and the weight distribution of C2C2 for the case that mgcd(m,k) is even.