论文标题
从嵌套$ f $ -adic扩展中的层次结构的最佳本地可回收代码
Optimal locally recoverable codes with hierarchy from nested $F$-adic expansions
论文作者
论文摘要
在本文中，我们构建了新的最佳分层本地可回收代码。我们的构建基于\ cite {ballentine2019代码，sasidharan2015codes}的想法的结合，并采用代数数理论方法的理论方法，可以更细微地调整中等规范的最小距离（允许最终代码的更大尺寸），以消除y尺寸的限制属性$ $ quative the Arith properies $ qy y n of quity properies $ qy n of quith propenties $ qy n of quith propenties $ qy的属性$ qy qu y q of quity的范围$ q. 等级制度。反过来，我们设法获得了基本场的大小$ q $的广泛参数的代码，以及层次结构大小，同时保持我们构建的代码的最佳性。
In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of \cite{ballentine2019codes,sasidharan2015codes} with an algebraic number theoretical approach that allows to give a finer tuning of the minimum distance of the intermediate code (allowing larger dimension of the final code), and to remove restrictions on the arithmetic properties of $q$ compared with the size of the locality sets in the hierarchy. In turn, we manage to obtain codes with a wide set of parameters both for the size $q$ of the base field, and for the hierarchy size, while keeping the optimality of the codes we construct.
