Weight Distribution of A p-ary Cyclic Code

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 $\mathbb{F}{p}$ with nonzeros $\alpha^{-1}$, $\alpha^{-(pk+1)}$ and $\alpha^{{-(p{3k}+1)}$,} where $\alpha$ is a primitive element of $\mathbb{F}{p^n}$