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arXiv · 2005.07577

Batch Codes from Affine Cartesian Codes and Quotient Spaces

Travis Baumbaugh·Haley Colgate·Timothy Jackman·Felice Manganiello
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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.

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Travis Baumbaugh, Haley Colgate, Timothy Jackman, Felice Manganiello. 2020-05-15. Batch Codes from Affine Cartesian Codes and Quotient Spaces. https://arxiv.org/abs/2005.07577

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