论文标题
绑定了LRC的最小场大小以及获得它的循环MR代码
A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It
论文作者
论文摘要
我们证明了对本地维修代码（LRCS）场地大小的新下限。此外，我们构建了循环的最大可回收（MR）代码。虽然已知的MR代码结构具有相同的参数，但它会产生非循环代码。此外，我们证明了必要的条件和足够条件，这些条件何时何时可以将已知的非循环MR代码排列为循环，从而证明我们的构造会产生带有新参数的环状MR代码。此外，使用我们对场大小的新结合，我们表明新的环状MR代码在某些情况下具有最佳的场大小。在某些情况下，其他已知的LRC也显示出具有最佳的场大小。
We prove a new lower bound on the field size of locally repairable codes (LRCs). Additionally, we construct maximally recoverable (MR) codes which are cyclic. While a known construction for MR codes has the same parameters, it produces non-cyclic codes. Furthermore, we prove both necessary conditions and sufficient conditions that specify when the known non-cyclic MR codes may be permuted to become cyclic, thus proving our construction produces cyclic MR codes with new parameters. Furthermore, using our new bound on the field size, we show that the new cyclic MR codes have optimal field size in certain cases. Other known LRCs are also shown to have optimal field size in certain cases.
