Cyclic codes over ℳ_4(𝔽_2 )
Journal of Applied Mathematics and Computing(2019)
摘要
In this article, keeping the huge research prospective of the study in mind, we consider the non-commutative ring ℳ_4(𝔽_2) , the set of all 4 × 4 matrices over the field 𝔽_2 and confirm that this ring is isomorphic with the ring 𝔽_16+u 𝔽_16+u^2 𝔽_16+u^3𝔽_16 , where u^4=0 . Besides, we develop the structure of cyclic codes and their generators over the ring. Also, making use of Gray map from ℳ_4(𝔽_2) to 𝔽_16^4 , we infer that the image of a cyclic code is a linear code. Finally, our findings are authenticated by suitable non-trivial examples.
更多查看译文
关键词
Matrix ring,Modules,Cyclic codes,Quaternary codes
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要