Self-dual Repeated Root Cyclic and Negacyclic Codes over Finite Fields

Kenza Guenda; T. Aaron Gulliver

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arXiv · 1207.3387

Self-dual Repeated Root Cyclic and Negacyclic Codes over Finite Fields

Kenza Guenda·T. Aaron Gulliver

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Abstract

In this paper we investigate repeated root cyclic and negacyclic codes of length $p^rm$ over $\mathbb{F}_{p^s}$ with $(m,p)=1$. In the case $p$ odd, we give necessary and sufficient conditions on the existence of negacyclic self-dual codes. When $m=2m'$ with $m'$ odd, we characterize the codes in terms of their generator polynomials. This provides simple conditions on the existence of self-dual negacyclic codes, and generalizes the results of Dinh \cite{dinh}. We also answer an open problem concerning the number of self-dual cyclic codes given by Jia et al. \cite{jia}.

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Kenza Guenda, T. Aaron Gulliver. 2012-07-14. Self-dual Repeated Root Cyclic and Negacyclic Codes over Finite Fields. https://arxiv.org/abs/1207.3387

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