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Hermitian-lifted codes

机译：赫米特翁举起的代码

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摘要

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 F-q2-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.
机译：在本文中，我们构建了局部恢复擦除的代码，具有高可用性和来自封闭曲线的恒定率。这些新的代码称为Hermitian升降的代码，是评估代码，评估组是仿射曲线上的F-Q2合理点的集合。新颖性是在评估的功能方面;它们是一套特殊的单体单体，限制与封闭曲线相交的线路的低度多项式。结果，对应于通过给定点的任何线的点对应的位置用作与该点对应的位置的恢复集。

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