摘要
研究了有限环F_2+F_2u+F_2u~2+F_2u~3上的线性码结构。定义了环F_2+F_2u+F_2u~2+F_2u~3上的线性码的Lee重量、Hamming重量、完全重量及对称重量计数器的概念,利用有限域上线性码和Gray映射的性质,给出了本环上的线性码之间的各重量分布的Macwilliams恒等式。最后,得到一类最优的线性码。
This paper studies the structure of the linear code over finite ring F_2+counting formulas of Lee weight, Hamming weight, and complete weight and symmetrized weight of linear codes over ring F_2+F_2 u +F_2 u~2+F_2 u~3. By the relationship of linear codes and the proposition of the Gray map, the paper give the Macwilliams identities between the linear codes. The study also obtains a class optimal linear codes.
引文
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