论文标题
提起芦苇 - 固体代码，并应用于批处理代码
Lifted Reed-Solomon Codes with Application to Batch Codes
论文作者
论文摘要
Guo，Kopparty和Sudan已通过提升仿射不变代码得出的错误校正代码进行了研究。提起的芦苇 - 固体（RS）代码被定义为对矢量空间中多项式的评估，通过要求它们限制到空间中的每一行，以作为RS代码的代码字。在本文中，我们调查了提起的RS代码，并讨论了它们对批处理代码的应用，这是在分布式存储系统中私人信息检索和负载平衡的背景下引入的。首先，我们提高了提起的RS代码的代码速率，以提升参数$ m \ ge 3 $和大型场尺寸。其次，提出了提出提起的RS代码的新的批处理代码的明确构造。对于某些参数制度，我们的代码在参数之间的权衡比以前已知的批次代码更好。
Guo, Kopparty and Sudan have initiated the study of error-correcting codes derived by lifting of affine-invariant codes. Lifted Reed-Solomon (RS) codes are defined as the evaluation of polynomials in a vector space over a field by requiring their restriction to every line in the space to be a codeword of the RS code. In this paper, we investigate lifted RS codes and discuss their application to batch codes, a notion introduced in the context of private information retrieval and load-balancing in distributed storage systems. First, we improve the estimate of the code rate of lifted RS codes for lifting parameter $m\ge 3$ and large field size. Second, a new explicit construction of batch codes utilizing lifted RS codes is proposed. For some parameter regimes, our codes have a better trade-off between parameters than previously known batch codes.
