Simple-root negacyclic codes of length $2p^n{\ell}^m$ over a finite field

Anuradha Sharma

doi:10.4134/JKMS.2015.52.5.965

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J. Korean Math. Soc. 2015; 52(5): 965-989

Printed September 1, 2015

https://doi.org/10.4134/JKMS.2015.52.5.965

Simple-root negacyclic codes of length $2p^n{\ell}^m$ over a finite field

Anuradha Sharma

Indian Institute of Technology Delhi

Abstract

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Abstract

Let $p$, $\ell$ be distinct odd primes, $q$ be an odd prime power with $\gcd(q,p)=\gcd(q,\ell)=1,$ and $m$, $n$ be positive integers. In this paper, we determine all self-dual, self-orthogonal and complementary-dual negacyclic codes of length $2p^n\ell^m$ over the finite field $\mathbb{F}_q$ with $q$ elements. We also illustrate our results with some examples.

Keywords: dual code, constacyclic codes, cyclotomic cosets

MSC numbers: 94B15