Group Factorizations and Information Theory

Abstract

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.