Ranks of propelinear perfect binary codes
Combinatorics
2012-11-01 v1 Information Theory
math.IT
Abstract
It is proven that for any numbers n=2^m-1, m >= 4 and r, such that n - log(n+1)<= r <= n excluding n = r = 63, n = 127, r in {126,127} and n = r = 2047 there exists a propelinear perfect binary code of length n and rank r.
Cite
@article{arxiv.1210.8253,
title = {Ranks of propelinear perfect binary codes},
author = {George K. Guskov and Ivan Yu. Mogilnykh and Faina I. Solov'eva},
journal= {arXiv preprint arXiv:1210.8253},
year = {2012}
}