论文标题
带有Hermitian的代码
Hermitian-Lifted Codes
论文作者
论文摘要
在本文中，我们构建了用于局部回收的局部回收，这些擦除率具有高可用性和恒定速率的率。这些新代码（称为赫尔米尼式代码）是评估代码，评估集是$ \ mathbb {f} _ {q^2} $ - 仿射曲线上的合理点。新颖的是要评估的功能。它们是一组特殊的单元，限制在与Hermitian曲线相交的线上的低度多项式。结果，与给定点的任何线相对应的位置作为与该点相对应的位置的恢复设置。
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.
