Self-dual 2-quasi negacyclic codes over finite fields

Abstract

In this paper, we investigate the existence and asymptotic properties 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 $q\not\equiv -1\left(\mathrm{mod}4\right)$. 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.