Let m, k be positive integers, p be an odd prime and $\pi $ be a primitive element of $\mathbb{ F}_{ p^m}$. In this paper, we determine the weight distribution of a family of cyclic codes $\mathcal{ C}_t$ over $\mathbb{ F}_p$, whose duals have two zeros $\pi^{ -t}$ and $-\pi^{ -t}$, where $t$ satisfies $t\equiv \frac{ p^k+1}{ 2}p^\tau \ ({ \rm mod}\ \frac{ p^m-1}{ 2}) $ for some $\tau \in \{ 0,1,\cdots, m-1\}$.
Categories: cs.IT math.IT