群体分解与信息论

2007 Information Theory and Applications Workshop Pub Date : 2007-10-22 DOI:10.1109/ITA.2007.4357607

U. Tamm

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引用次数: 1

摘要

群G的分解是子集(A1, A2，…，Ar)的集合，使得G中的每个元素G都有一个唯一的表示G =a1ldr a2ldr…ldrar，其中a1 = Ai，当i = 1，…我们将考察群分解在信息论中的几个应用。它们出现在整数码的证型分析中，对LDPC码具有重要意义的几个大周长图可以用群分解构造出来，各种密码系统都基于它们。

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Group Factorizations and Information Theory

A factorization of a group G is a collection of subsets (A₁, A₂,...,A_r) such that every element g isin G has a unique representation g =a₁ldr a₂ldr...ldra_r where a₁ isin A_i for i = 1,..., r. We shall survey several applications of group factorizations in information theory. They occur in the analysis of syndromes of integer codes, several graphs with large girth important for LDPC codes can be constructed using group factorizations, and various cryptosystems are based on them.

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2007 Information Theory and Applications Workshop

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