Hermitian-Lifted Codes
Information Theory
2024-02-06 v1 math.IT
Abstract
In this paper, we construct codes for local recovery of erasures with high availability and constant-bounded rate from the Hermitian curve. These new codes, called Hermitian-lifted codes, are evaluation codes with evaluation set being the set of -rational points on the affine curve. The novelty is in terms of the functions to be evaluated; they are a special set of monomials which restrict to low degree polynomials on lines intersected with the Hermitian curve. As a result, the positions corresponding to points on any line through a given point act as a recovery set for the position corresponding to that point.
Keywords
Cite
@article{arxiv.2006.05558,
title = {Hermitian-Lifted Codes},
author = {Hiram H. López and Beth Malmskog and Gretchen L Matthews and Fernando Piñero-González and Mary Wootters},
journal= {arXiv preprint arXiv:2006.05558},
year = {2024}
}