二元非线性(64,2^(32),14)码的代数译码研究

On the Algebraic Decoding of the Binary Nonlinear(64,2^(32),14) Code

环上线性分组码基于Lee度量译码是环上线性分组码研究方向上的一个重要课题。文章在总结和借鉴现有环上线性分组码基于Lee度量译码的研究成果的基础上,解决了Z4-线性的二元非线性(64,232,14)码的译码问题。二元非线性(64,232,14)码是已知最好的(64,232)码,它可看作Z4上一个能纠正Lee重不超过6的所有错误的特殊循环码的二元Gray像。

Decoding codes over tings with Lee metric is very important in coding theory. In this paper, we creatively solve the problem of decoding the （64,2^32, 14） code which is binary nonlinear but Z4-linear, based on much famous work done by other researchers. The binary nonlinear （64,232, 14） code is the best （64,232） code that is presently known, and it is an image via Gray map of a specific cyclic codes over Z4 which can correct all errors with Lee weight ≤ 6.