Constructing Partial MDS Codes from Reducible Algebraic Curves
Tristram Bogart, Anna-Lena Trautmann, David Karpuk, Alessandro Neri, Mauricio Velasco · SIAM Journal on Discrete Mathematics · 2021
We propose reducible algebraic curves as a mechanism to construct partial maximum distance separable 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.