Long Nonbinary Codes Exceeding the Gilbert - Varshamov Bound for any Fixed Distance
Information Theory
2007-07-13 v3 math.IT
Abstract
Let A(q,n,d) denote the maximum size of a q-ary code of length n and distance d. We study the minimum asymptotic redundancy \rho(q,n,d)=n-log_q A(q,n,d) as n grows while q and d are fixed. For any d and q<=d-1, long algebraic codes are designed that improve on the BCH codes and have the lowest asymptotic redundancy \rho(q,n,d) <= ((d-3)+1/(d-2)) log_q n known to date. Prior to this work, codes of fixed distance that asymptotically surpass BCH codes and the Gilbert-Varshamov bound were designed only for distances 4,5 and 6.
Cite
@article{arxiv.cs/0406039,
title = {Long Nonbinary Codes Exceeding the Gilbert - Varshamov Bound for any Fixed Distance},
author = {Sergey Yekhanin and Ilya Dumer},
journal= {arXiv preprint arXiv:cs/0406039},
year = {2007}
}
Comments
Submitted to IEEE Trans. on Info. Theory