论文标题
最佳$（r，δ）$ - 单元代码的LRC及其子场 - subcodes
Optimal $(r,δ)$-LRCs from monomial-Cartesian codes and their subfield-subcodes
论文作者
论文摘要
我们研究了单一 - 牙犯代码（MCC），可以将其视为$（r，δ）$ - 局部可回收的代码（LRCS）。这些代码具有最小距离的自然界限，我们确定那些产生$（r，δ）$ - 最佳LRC的距离，实际上是$（r，δ）$ - 最佳。 MCC的大型亚家族允许具有某些最佳MCC的相同参数但在较小的支撑域中的子场填充。这个事实使我们能够确定许多新的$（R，δ）$ - 最佳LRC及其参数。
We study monomial-Cartesian codes (MCCs) which can be regarded as $(r,δ)$-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to $(r,δ)$-optimal LRCs for that distance, which are in fact $(r,δ)$-optimal. A large subfamily of MCCs admits subfield-subcodes with the same parameters of certain optimal MCCs but over smaller supporting fields. This fact allows us to determine infinitely many sets of new $(r,δ)$-optimal LRCs and their parameters.
