论文标题
一个通用的MSRD代码和PMDS代码，该代码具有较小的摩尔矩阵的场尺寸较小的场地
A general family of MSRD codes and PMDS codes with smaller field sizes from extended Moore matrices
论文作者
论文摘要
我们构建了六个新的明确族，具有线性最大总和距离（MSRD）代码，每个代码在所有已知的MSRD代码中的某些参数制度中具有最小的场大小。使用它们和作者的先前结果，我们提供了两个新的明确系列局部MDS（PMDS）代码，其场尺寸较小，比以前的PMDS代码较小。我们的方法是表征评估点，这些评估点将扩展的摩尔矩阵转变为线性MSRD代码的奇偶校验检查矩阵。然后，我们从具有良好的锤态参数的代码中产生此类序列。使用MDS代码，Hamming代码，BCH代码和三个代数几何代码获得了六个具有较小场尺寸的线性MSRD代码的新家族。根据最低总和距离$ 3 $的HAMMING代码的MSRD代码符合Byrne等人的最新限制。
We construct six new explicit families of linear maximum sum-rank distance (MSRD) codes, each of which has the smallest field sizes among all known MSRD codes for some parameter regime. Using them and a previous result of the author, we provide two new explicit families of linear partial MDS (PMDS) codes with smaller field sizes than previous PMDS codes for some parameter regimes. Our approach is to characterize evaluation points that turn extended Moore matrices into the parity-check matrix of a linear MSRD code. We then produce such sequences from codes with good Hamming-metric parameters. The six new families of linear MSRD codes with smaller field sizes are obtained using MDS codes, Hamming codes, BCH codes and three Algebraic-Geometry codes. The MSRD codes based on Hamming codes, of minimum sum-rank distance $ 3 $, meet a recent bound by Byrne et al.
