Repeated-Root Self-Dual Negacyclic Codes over Finite Fields

Abstract:

      Let $F_{q}$ be a finite field with $q=p^{m}$, where $p$ is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over $F_{q}$. The enumeration of such codes is investigated. We obtain all the self-dual negacyclic codes of length $2^{a}p^{r}$ over $F_{q}$, $a\geq1$. The construction of self-dual negacyclic codes of length $2^{a}bp^{r}$ over $F_{q}$ is also provided, where ${\rm gcd}(2,b)={\rm gcd}(b,p)=1$ and $a\geq1$.