Cyclic and constacyclic self-dual codes over $R_k$
Bull. Korean Math. Soc. 2017 Vol. 54, No. 4, 1111-1122
https://doi.org/10.4134/BKMS.b150764
Published online July 31, 2017
Suat Karadeniz, Ismail Gokhan Kelebek, and Bahattin Yildiz
Fatih University, Fatih University, Fatih University
Abstract : 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.
Keywords : cyclic codes, constacyclic codes, cyclic self-dual codes, lift, projection
MSC numbers : Primary 94B05, 94B99; Secondary 11T71, 13M99
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