On the weight distributions of a class of cyclic codes

Let m and k be two positive integers such that v(2)(m) = v(2)(k), where v(2)(.) denotes the 2-valuation function, and let alpha be a primitive element of F-p2m. Let C be a cyclic code over F-p with a parity-check polynomial h(1)(X)h(2)(X)h(3)(X) is an element of F-p2m [x], where h(1)(x), h(2)(x) and h(3)(x) are the minimal polynomials of alpha(-pk+1/2), -alpha(-pk+1/2) and alpha(-pm+1/2) over F-p respectively. In this paper, we determine the weight distribution and the complete weight distribution of the code C. (C) 2017 Elsevier B.V. All rights reserved.