Constructing Partial MDS Codes from Reducible Curves
Information Theory
2020-07-30 v1 Algebraic Geometry
Combinatorics
math.IT
Abstract
We propose reducible algebraic curves as a mechanism to construct Partial MDS (PMDS) codes geometrically. We obtain new general existence results, new explicit constructions and improved estimates on the smallest field sizes over which such codes can exist. Our results are obtained by combining ideas from projective algebraic geometry, combinatorics and probability theory.
Cite
@article{arxiv.2007.14829,
title = {Constructing Partial MDS Codes from Reducible Curves},
author = {Tristram Bogart and Anna-Lena Horlemann-Trautmann and David Karpuk and Alessandro Neri and Mauricio Velasco},
journal= {arXiv preprint arXiv:2007.14829},
year = {2020}
}
Comments
25 pages