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.
Copyright © 2019 Abdulla Eid, Khalid Amin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
A. Eid, K. Amin, Abelian group factorization from perfect codes, J. Math. Comput. Sci. 9 (2019), 755–763. https://doi.org/10.28919/jmcs/4221
BibTeX
@article{Eid2019,
author = {Eid, Abdulla and Amin, Khalid},
title = {Abelian group factorization from perfect codes},
journal = {J. Math. Comput. Sci.},
volume = {9},
year = {2019},
pages = {755--763},
doi = {10.28919/jmcs/4221}
}