Batch Codes from Affine Cartesian Codes and Quotient Spaces [article]

Travis Baumbaugh, Haley Colgate, Timothy Jackman, Felice Manganiello
2020 arXiv   pre-print
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
more » ... p to one more than the dimension of the space of the ambient space.
arXiv:2005.07577v1 fatcat:avy3v3lb4zdzhit5uhnclau4yy