Weight distribution of some cyclic codes

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