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Cyclic and constacyclic self-dual codes over R_k
Suat Karadeniz,Ismail Gokhan Kelebek,Bahattin Yildiz 대한수학회 2017 대한수학회보 Vol.54 No.4
In this work, we consider constacyclic and cyclic self-dual codes over the rings $R_k$. We start with theoretical existence results for constacyclic and cyclic self-dual codes of any length over $R_k$ and then construct cyclic self-dual codes over $R_1 = \F_2+u\F_2$ of even lengths from lifts of binary cyclic self-dual codes. We classify all free cyclic self-dual codes over $R_1$ of even lengths for which non-trivial such codes exist. In particular we demonstrate that our constructions provide a counter example to a claim made by Batoul et al. in \cite{Batoul} and we explain why their claim fails.
CYCLIC AND CONSTACYCLIC SELF-DUAL CODES OVER R<sub>k</sub>
Karadeniz, Suat,Kelebek, Ismail Gokhan,Yildiz, Bahattin Korean Mathematical Society 2017 대한수학회보 Vol.54 No.4
In this work, we consider constacyclic and cyclic self-dual codes over the rings $R_k$. We start with theoretical existence results for constacyclic and cyclic self-dual codes of any length over $R_k$ and then construct cyclic self-dual codes over $R_1={\mathbb{F}}_2+u{\mathbb{F}}_2$ of even lengths from lifts of binary cyclic self-dual codes. We classify all free cyclic self-dual codes over $R_1$ of even lengths for which non-trivial such codes exist. In particular we demonstrate that our constructions provide a counter example to a claim made by Batoul et al. in [1] and we explain why their claim fails.