Repeated-root constacyclic codes of length $2\ell^mp^n$

TL;DR

This paper characterizes the structure of constacyclic codes of length $2 ext{l}^ ext{m} ext{p}^ ext{n}$ over finite fields, including duals, and identifies all self-dual and complementary dual codes for these lengths.

Contribution

It provides a comprehensive structural analysis of repeated-root constacyclic codes of specified length over finite fields, including dual and self-dual codes, which was previously unexplored.

Findings

All linear complementary dual constacyclic codes are identified.

All self-dual constacyclic codes of the specified length are characterized.

The structure of these codes is described in terms of generator polynomials.

Abstract

For any different odd primes $\ell$ and $p$, structure of constacyclic codes of length $2\ell^mp^n$ over a finite field $\mathbb F_q$ of characteritic $p$ and their duals is established in term of their generator polynomials. Among other results, all linear complimentary dual and self-dual constacyclic codes of length $2\ell^mp^n$ over $\mathbb F_q$ are obtained.