论文标题
近MDS代码的构造是最佳的本地可回收代码
Constructions of near MDS codes which are optimal locally recoverable codes
论文作者
论文摘要
具有参数的线性代码$ [n，k，n-k] $几乎是可分开的最大距离（简称AMD）。 AMDS代码的双重代码也称为AMDS，称为接近最大距离（短）代码（NMD）代码。 NMDS代码在有限的几何形状，组合学，加密和数据存储中具有不错的应用。在本文中，我们首先介绍了NMDS代码的几种结构，并确定其重量枚举器。特别是，某些结构产生的NMDS代码具有相同的参数，但重量枚举不同。然后，我们确定NMDS代码的位置，并获得许多距离最佳和最佳范围的局部修复代码的家族。
A linear code with parameters $[n,k,n-k]$ is said to be almost maximum distance separable (AMDS for short). An AMDS code whose dual is also AMDS is referred to as an near maximum distance separable (NMDS for short) code. NMDS codes have nice applications in finite geometry, combinatorics, cryptography and data storage. In this paper, we first present several constructions of NMDS codes and determine their weight enumerators. In particular, some constructions produce NMDS codes with the same parameters but different weight enumerators. Then we determine the locality of the NMDS codes and obtain many families of distance-optimal and dimension-optimal locally repairable codes.
