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arXiv · 2006.05558

Hermitian-Lifted Codes

Hiram H. López·Beth Malmskog·Gretchen L Matthews·Fernando Piñero-González·Mary Wootters
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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 $\mathbb{F}_{q^2}$-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.

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Hiram H. López, Beth Malmskog, Gretchen L Matthews, Fernando Piñero-González, Mary Wootters. 2020-06-09. Hermitian-Lifted Codes. https://doi.org/10.1007/s10623-020-00836-6

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