Open AccessSkew Cyclic Codes over a Non‐chain Ring
Author(s) -
Shi Minjia,
Yao Ting,
Solé Patrick
Publication year - 2017
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2017.03.008
Subject(s) - skew , idempotence , ring (chemistry) , generator (circuit theory) , cyclic code , polynomial ring , code (set theory) , polynomial code , mathematics , dual (grammatical number) , discrete mathematics , computer science , polynomial , algorithm , linear code , power (physics) , telecommunications , block code , physics , programming language , chemistry , organic chemistry , art , mathematical analysis , decoding methods , literature , quantum mechanics , set (abstract data type)
We study skew cyclic codes over a nonchain ring, which generalizes our previous results in IEICE Trans. on Fundamentals of Electronic Communications and Computer Sciences , 2015. We describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over the ring by a decomposition theorem. The generator polynomial of the dual code of a skew cyclic code are obtained. Moreover, the idempotent generators of skew cyclic codes are considered. Some examples are also presented to illustrate the discussed results.