Abelian group factorization from perfect codes

Abstract

In this paper, we give a factorization of certain p–groups using non–trivial perfect codes (Hamming and Golay codes). The factorization consists of two sets, one corresponding to the perfect code and the other corresponding to the codewords in the Hamming sphere with center at the zero codeword and radius one (Hamming code) and three (Golay code). Non–perfect codes are also considered in such construction and we give the necessary condition for the factorization in terms of the parity check matrix of the code.