Weight Distribution of Some Cyclic Codes

Abstract

In this paper, for an odd prime p such that p 3 mod 4, odd n, and d = (p(n) + 1)/(p(k) + 1) + (p(n) - 1)/2 with k vertical bar n, the value distribution of the exponential sum S(a, b) when a and b run through F-pn is calculated. The weight distribution of the relevant cyclic code C over F-p with the length L = p(n) - 1 and the dimension dim(Fp)C - 2n is also derived. Our result generalizes the case in [5].