Self-dual 2-quasi Negacyclic Codes over Finite Fields

In this paper, we investigate the existence and asymptotic property of self-dual $2$-quasi negacyclic codes of length $2n$ over a finite field of cardinality $q$. When $n$ is odd, we show that the $q$-ary self-dual $2$-quasi negacyclic codes exist if and only if $q\,{\not\equiv}-\!1~({\rm mod}~4)$. When $n$ is even, we prove that the $q$-ary self-dual $2$-quasi negacyclic codes always exist. By using the technique introduced in this paper, we prove that $q$-ary self-dual $2$-quasi negacyclic codes are asymptotically good.