Monday 25th of September 2017
 

The Gray images of linear codes over the ring F3+vF3+v2F3


Yazhou Xiong, Shujie Yun, Jingyuan Xing and Xiaofang Xu

In this work, we focus on the Gray images of the linear codes over the ring , which is a finite chain ring. Firstly, we give the generator matrix of the linear code and its dual code over the ring . Secondly, we define an isomorphism from to and obtain the generator matrix of the linear code and its dual code over the ring . Then, we define a Gray map from to , and obtain Gray image from the generator matrix of the linear code over the ring . Finally, we prove that the Gray images of cyclic codes are quasi-cyclic codes over .

Keywords: Linear codes, Generator matrix, Gray image, Dual code

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ABOUT THE AUTHORS

Yazhou Xiong
School of Economics and management, Hubei Polytechnic University

Shujie Yun
Department of basic, Henan Mechanical and Electrical Engineering College

Jingyuan Xing
School of Economics and management, Hubei Polytechnic University

Xiaofang Xu
School of Mathematics and Physics, Hubei Polytechnic University


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