Linear Codes Over a Non-Chain Ring and the MacWilliams Identities

IEEE Access

Rongsheng Wu¹  Tiantian Li¹  Juan Xu² 

[1] School of Mathematical Sciences, Anhui University, Hefei, China;School of Mathematics and Physics, Anqing Normal University, Anqing, China;

关键词: Generator matrix;    linear code;    MacWilliams identity;    weight enumerator;   

DOI  :  10.1109/ACCESS.2020.2992586

来源: DOAJ

【 摘 要 】

This paper is concerned with the linear codes over the non-chain ring R=F₂[v]/〈v⁴-v〉. First, several weight enumerators over R are defined. Then the MacWilliams identity is obtained, which can establish an important relation respect to the complete weight enumerators. Meanwhile, the symmetric weight enumerators between linear code and its dual over R are established by the Gray map from Rⁿ to F₂⁴ⁿ. Finally, several examples are given to illustrate our main results and some open problems are also proposed.

【 授权许可】

Unknown