标题： 从双椭圆曲线中获得的最优和几乎最优局部可修复码 显示英文标题

标题： Optimal and Almost Optimal Locally Repairable Codes from Hyperelliptic Curves

摘要： 局部可修复码在现代大规模分布式云存储系统和其他各种领域中具有广泛的应用。 通过利用椭圆曲线的一些代数结构，李等人开发了一系列长度可以扩展到$q+2\sqrt{q}$的$q$-元最优局部可修复码。 在本文中，我们将他们的方法推广到亏格为$2$的双椭圆曲线，从而构造出几个新的$q$-元最优或几乎最优的局部可修复码家族。 我们的码具有可以接近$q+4\sqrt{q}$的长度，局部性可以达到高达$239$。 显示英文摘要

摘要： Locally repairable codes are widely applicable in contemporary large-scale distributed cloud storage systems and various other areas. By making use of some algebraic structures of elliptic curves, Li et al. developed a series of $q$-ary optimal locally repairable codes with lengths that can extend to $q+2\sqrt{q}$. In this paper, we generalize their methods to hyperelliptic curves of genus $2$, resulting in the construction of several new families of $q$-ary optimal or almost optimal locally repairable codes. Our codes feature lengths that can approach $q+4\sqrt{q}$, and the locality can reach up to $239$.