Weight Distribution of A p-ary Cyclic Code

Abstract

For an odd prime $p$ and two positive integers $n\ge 3$ and $k$ with $\frac{n}{\gcd (n,k)}$ being odd, the paper determines the weight distribution of a $p$-ary cyclic code $\mathcal{C}$ over ${\mathbb{F}}_p$ with nonzeros ${\alpha }^{-1}$, ${\alpha }^{-(p^k+1)}$ and ${\alpha }^{-(p^{3k}+1)}$, where $\alpha$ is a primitive element of ${\mathbb{F}}_{p^n}$

15 pages