论文标题
小领域上的稀疏和平衡的MDS代码
Sparse and Balanced MDS Codes over Small Fields
论文作者
论文摘要
具有稀疏且平衡的发电机矩阵的最大距离可分离（MDS）代码在分布式存储系统中吸引了平衡和最小化计算负载。此类代码已经通过大型田地上的芦苇 - 固体代码构建。在本文中，我们专注于小领域。我们证明存在$ [n，k] _q $ mds代码，该代码具有稀疏且平衡的生成器矩阵，对于任何$ q \ geq n $，前提是$ n \ leq 2k $，通过设计几种具有复杂性在$ k $和$ n $中的多项式时间运行的算法。
Maximum Distance Separable (MDS) codes with a sparse and balanced generator matrix are appealing in distributed storage systems for balancing and minimizing the computational load. Such codes have been constructed via Reed-Solomon codes over large fields. In this paper, we focus on small fields. We prove that there exists an $[n,k]_q$ MDS code that has a sparse and balanced generator matrix for any $q\geq n$ provided that $n\leq 2k$, by designing several algorithms with complexity running in polynomial time in $k$ and $n$.
