Bull. Korean Math. Soc. 2017; 54(4): 1111-1122
Online first article July 10, 2017 Printed July 31, 2017
https://doi.org/10.4134/BKMS.b150764
Copyright © The Korean Mathematical Society.
Suat Karadeniz, Ismail Gokhan Kelebek, and Bahattin Yildiz
Fatih University, Fatih University, Fatih University
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
2019; 56(3): 609-619
2019; 56(2): 419-437
2019; 56(6): 1385-1422
2019; 56(2): 285-301
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd