Weight Distribution of A p-ary Cyclic Code

Abstract: For an odd prime $p$ and two positive integers $n\geq 3$ and $k$ with $\frac{n}{{\rm gcd}(n,k)}$ being odd, the paper determines the weight distribution of a $p$-ary cyclic code $\mathcal{C}$ over $\mathbb{F}<em>{p}$ with nonzeros $\alpha<sup>{-1}$, $\alpha<sup>{-(p<sup>k+1)}$ and $\alpha<sup>{-(p<sup>{3k}+1)}$, where $\alpha$ is a primitive element of $\mathbb{F}</em>{p<sup>n}$