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