【摘要】 研究了有限环F₂+F₂u+F₂u²+F₂u³上的线性码结构。定义了环F₂+F₂u+F₂u²+F₂u³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。更多还原

【Abstract】 This paper studies the structure of the linear code over finite ring F₂+counting formulas of Lee weight, Hamming weight, and complete weight and symmetrized weight of linear codes over ring F₂+F₂ u +F₂ u²+F₂ u³. 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.更多还原