高维大码距Hamilton阵列编码理论与综合算法
The theory of hamilton array codes for high dimension and big hamming distance and the synthesis algorithm
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摘要: 该文定义了高维大码距Hamilton阵列编码理论的基本概念，分析了d=2k-1(k3)类型和d=2k(k3)类型阵列编码的Hamilton逻辑拓扑结构模型和一般Hamilton阵列编码的存在拓扑条件，并给出d=2k-1(k3)与d=2k(k3)高阶高维Hamilton阵列编码的构造原理和综合算法。文中还讨论了两类模型的区别，以及实例设计，这为新型阵列密码研究提供一个新方向。Abstract: In this paper, the theory of Hamilton array codes for high dimension and big Hamming distance is proposed. The model of logical topology structure for d- 2k-l,d=2k(k 3) types and the existence topology condition for general high order SM array codes are analyzed. The construction principle and the synthesis algorithm of SM array codes for d=2k- 1 and d=2k(k 3) high dimension and high order are discussed. Finally, the distinction between the two models and the example design are given. The result provides a new direction for a class of new type array ciphers research.
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