基于仿射笛卡尔码和商空间的批码
Batch Codes from Affine Cartesian Codes and Quotient Spaces
摘要：
仿射笛卡尔码是通过在有限域的有限子集的笛卡尔积上计算多元多项式来定义的。在这项工作中，我们研究这些代码作为批处理代码的属性。我们认为恢复集是由在特定方向上对齐的点定义的，并且桶是从评估点的环境空间的子空间的陪集导出的。我们能够证明，在这些条件下，一个仿射笛卡尔代码是能够满足查询的大小比周围空间的空间的维度多一个。
英文摘要：
Affine Cartesian codes are defined by evaluating multivariate polynomials at a cartesian product of finite subsets of a finite field. In this work we examine properties of these codes as batch codes. We consider the recovery sets to be defined by points aligned on a specific direction and the buckets to be derived from cosets of a subspace of the ambient space of the evaluation points. We are able to prove that under these conditions, an affine Cartesian code is able to satisfy a query of size up to one more than the dimension of the space of the ambient space.
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