Cyclic and constacyclic codes over a non-chain ring
DOI:
https://doi.org/10.13069/jacodesmath.31486Keywords:
Non-chain rings, Linear codes, Cyclic codes, Constacyclic codes, MacWilliams type identityAbstract
In this study, we consider linear and especially cyclic codes over the non-chain ring $\mathbb{Z}_{p}[v]/\langle v^{p}-v\rangle$ where $p$ is a prime. This is a generalization of the case $p=3.$ Further, in this work the structure of constacyclic codes are studied as well. This study takes advantage mainly from a Gray map which preserves the distance between codes over this ring and $p$-ary codes and moreover this map enlightens the structure of these codes. Furthermore, a MacWilliams type identity is presented together with some illustrative examples.
Received: 21 April 2014 | Accepted: 26 August 2014
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