论文标题
来自载体笛卡尔代码和商空间的批量代码
Batch Codes from Affine Cartesian Codes and Quotient Spaces
论文作者
论文摘要
载载笛卡尔代码是通过评估有限场有限亚集的笛卡尔产物的多元多项式来定义的。在这项工作中，我们将这些代码的属性视为批处理代码。我们认为恢复集由在特定方向上对齐的点来定义，而要衍生自评估点环境空间子空间的coset的存储桶。我们能够证明，在这些条件下，载载笛卡尔代码能够满足大小的查询，最高比环境空间的空间的尺寸高。
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.
