A Class of Nonbinary Codes and Their Weight Distribution

Abstract: In this paper, for an even integer $n\geq 4$ and any positive integer $k$ with ${\rm gcd}(n/2,k)={\rm gcd}(n/2-k,2k)=d$ being odd, a class of $p$-ary codes $\mathcal{C}^k$ is defined and their weight distribution is completely determined, where $p$ is an odd prime. As an application, a class of nonbinary sequence families is constructed from these codes, and the correlation distribution is also determined.