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.
翻译:在本文中,我们构建了新的最佳等级可在当地回收的代码。 我们的构建基于\ cite{ballentine2019code,sasidharan2015codes}的概念与代数理论方法的结合,该理论方法可以对中间代码的最低距离进行细微调整(允许最终代码的更大尺寸),并取消相对于等级中地点组的规模对美元算术属性的限制。 反过来,我们设法获得具有广泛参数的代码,包括基础字段的大小($q)和等级大小,同时保持我们构建的代码的最佳性。