Self-dual 2-quasi Negacyclic Codes over Finite Fields

TL;DR

This paper studies the existence and properties of self-dual 2-quasi negacyclic codes over finite fields, establishing conditions for their existence and demonstrating their asymptotic goodness.

Contribution

It provides new existence criteria for self-dual 2-quasi negacyclic codes based on the parity of length and field characteristics, and proves their asymptotic goodness.

Findings

Self-dual 2-quasi negacyclic codes exist when n is even.

Existence depends on the congruence of q modulo 4 when n is odd.

These codes are proven to be asymptotically good.

Abstract

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.