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Optimum commutative group codes

机译:最佳交换组码

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摘要

A method for finding an optimum n-dimensional commutative group code of a given order M is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of non-isometric cases to be analyzed. The classical factorization of matrices into Hermite and Smith normal forms and also basis reduction of lattices are used to characterize isometric commutative group codes. Several examples of optimum commutative group codes are also presented.
机译:提出了一种寻找给定阶数M的最优n维可交换群码的方法。该方法探索了与这些代码相关的晶格的结构,并显着减少了要分析的非等距情况的数量。将矩阵经典分解为Hermite和Smith范式以及格的基本约简,以表征等距可交换组代码。还给出了最佳交换组码的几个例子。

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