A Class of Nonbinary Codes and Their Weight Distribution

Abstract

In this paper, for an even integer $n\ge 4$ and any positive integer $k$ with $\gcd (n/2,k)=\gcd (n/2-k,2k)=d$ 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.

18 pages