On lifting perfect codes
Information Theory
2015-10-25 v1 Discrete Mathematics
Combinatorics
math.IT
Abstract
In this paper we consider completely regular codes, obtained from perfect (Hamming) codes by lifting the ground field. More exactly, for a given perfect code C of length n=(q^m-1)/(q-1) over F_q with a parity check matrix H_m, we define a new code C_{(m,r)} of length n over F_{q^r}, r > 1, with this parity check matrix H_m. The resulting code C_{(m,r)} is completely regular with covering radius R = min{r,m}. We compute the intersection numbers of such codes and, finally, we prove that Hamming codes are the only codes that, after lifting the ground field, result in completely regular codes.
Keywords
Cite
@article{arxiv.1002.0295,
title = {On lifting perfect codes},
author = {Josep Rifà and Victor Zinoviev},
journal= {arXiv preprint arXiv:1002.0295},
year = {2015}
}
Comments
Submitted to IEEE Transactions on Information Theory