English

Reed-Solomon codes over small fields with constrained generator matrices

Combinatorics 2019-01-30 v2 Information Theory math.IT

Abstract

We give constructions of some special cases of [n,k][n,k] Reed-Solomon codes over finite fields of size at least nn and n+1n+1 whose generator matrices have constrained support. Furthermore, we consider a generalisation of the GM-MDS conjecture proposed by Lovett in 2018. We show that Lovett's conjecture is false in general and we specify when the conjecture is true.

Keywords

Cite

@article{arxiv.1808.06306,
  title  = {Reed-Solomon codes over small fields with constrained generator matrices},
  author = {Gary Greaves and Jeven Syatriadi},
  journal= {arXiv preprint arXiv:1808.06306},
  year   = {2019}
}

Comments

21 pages

R2 v1 2026-06-23T03:37:58.856Z