Batch Codes from Affine Cartesian Codes and Quotient Spaces
Information Theory
2020-05-18 v1 math.IT
Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2005.07577,
title = {Batch Codes from Affine Cartesian Codes and Quotient Spaces},
author = {Travis Baumbaugh and Haley Colgate and Timothy Jackman and Felice Manganiello},
journal= {arXiv preprint arXiv:2005.07577},
year = {2020}
}