Hermitian-Lifted Codes

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 \(\mathbb{F}_{q^2}\)-rational points on the affine cur...

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Bibliographic Details
Published in:arXiv.org 2020-06
Main Authors: López, Hiram H, Malmskog, Beth, Matthews, Gretchen L, Piñero-González, Fernando, Wootters, Mary
Format: Article
Language:English
Subjects:
Mathematical analysis
Polynomials
Recovery
Online Access:Get full text
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Summary: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 \(\mathbb{F}_{q^2}\)-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.
ISSN:2331-8422
DOI:10.48550/arxiv.2006.05558