(1+uv)-Cyclic Codes Over F2+uF2+vF2+uvF2
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摘要: 该文定义了有限非链环R=F2+uF2+vF2+uvF2上(1+uv)-循环码的相关概念，讨论了其与该环上循环码的关系，证明了此环上(1+uv)-循环码在关于齐次重量的等距Gray映射hom下的二元象是一个长为8n的4-准循环码, 并由此映射得到了一些好的二元线性准循环码。
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关键词:
- 循环码 /
- (1+uv)-循环码 /
- Gray映射 /
- 准循环码
Abstract: (1+uv)-cyclic codes over F2+uF2+vF2+uvF2 is defined, and the relations between(1+uv)- cyclic codes and cyclic codes is discussed. It is proved that the binary image on isometric Gray maphomof a (1+uv)-cyclic code of length n over R is a linear quasi-cyclic code of index 4 and of length 8n. Furthermore, some optimal binary linear quasi-cyclic codes are obtained.-
Key words:
- Cyclic codes /
- (1+uv)-cyclic code /
- Gray map /
- Quasi-cyclic code
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