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Batch Codes from Affine Cartesian Codes and Quotient Spaces

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Part of the Lecture Notes in Computer Science book series (LNSC,volume 13129)

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 ambient space.

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  • DOI: 10.1007/978-3-030-92641-0_1
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Acknowledgments

This research was partially supported by the National Science Foundation under grant DMS-1547399.

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Correspondence to Felice Manganiello .

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Baumbaugh, T.A., Colgate, H., Jackman, T., Manganiello, F. (2021). Batch Codes from Affine Cartesian Codes and Quotient Spaces. In: Paterson, M.B. (eds) Cryptography and Coding. IMACC 2021. Lecture Notes in Computer Science(), vol 13129. Springer, Cham. https://doi.org/10.1007/978-3-030-92641-0_1

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  • DOI: https://doi.org/10.1007/978-3-030-92641-0_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92640-3

  • Online ISBN: 978-3-030-92641-0

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