Optimum Linear Codes with Support Constraints over Small Fields
Information Theory
2018-03-13 v1 math.IT
Abstract
We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the generator matrix. We show that the largest minimum distance can be achieved by a subcode of a Reed-Solomon code of small field size. As a by-product of this result, we settle the GM-MDS conjecture of Dau et. al. in the affirmative.
Cite
@article{arxiv.1803.03752,
title = {Optimum Linear Codes with Support Constraints over Small Fields},
author = {Hikmet Yildiz and Babak Hassibi},
journal= {arXiv preprint arXiv:1803.03752},
year = {2018}
}