Asymptotic improvement of the Gilbert-Varshamov bound for linear codes
Information Theory
2008-09-26 v1 math.IT
Abstract
The Gilbert-Varshamov bound states that the maximum size A_2(n,d) of a binary code of length n and minimum distance d satisfies A_2(n,d) >= 2^n/V(n,d-1) where V(n,d) stands for the volume of a Hamming ball of radius d. Recently Jiang and Vardy showed that for binary non-linear codes this bound can be improved to A_2(n,d) >= cn2^n/V(n,d-1) for c a constant and d/n <= 0.499. In this paper we show that certain asymptotic families of linear binary [n,n/2] random double circulant codes satisfy the same improved Gilbert-Varshamov bound.
Keywords
Cite
@article{arxiv.0708.4164,
title = {Asymptotic improvement of the Gilbert-Varshamov bound for linear codes},
author = {Philippe Gaborit and Gilles Zemor},
journal= {arXiv preprint arXiv:0708.4164},
year = {2008}
}
Comments
Submitted to IEEE Transactions on Information Theory