On the weight distributions of a class of cyclic codes

Let m and k be two positive integers such that v2(m)=v2(k), where v2(⋅) denotes the 2-valuation function, and let α be a primitive element of Fp2m. Let C be a cyclic code over Fp with a parity-check polynomial h1(x)h2(x)h3(x)∈Fp2m[x], where h1(x), h2(x) and h3(x) are the minimal polynomials of α−pk+12, −α−pk+12 and α−pm+12 over Fp respectively. In this paper, we determine the weight distribution and the complete weight distribution of the code C.