On the Affine Permutation Group of Certain Decreasing Cartesian Codes

Eduardo Camps-Moreno; Hiram H. López; Eliseo Sarmiento; Ivan Soprunov

doi:10.1109/ISIT57864.2024.10619396

On the Affine Permutation Group of Certain Decreasing Cartesian Codes

Eduardo Camps-Moreno
, Hiram H. López
, Eliseo Sarmiento
, Ivan Soprunov

Virginia Tech
Instituto Politécnico Nacional

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A decreasing Cartesian code is defined by evaluating a monomial set closed under divisibility on a Cartesian set. Some well-known examples are the Reed-Solomon, Reed-Muller, and (some) toric codes. The affine permutations consist of the permutations of the code that depend on an affine transformation. In this work, we study the affine permutations of some decreasing Cartesian codes, including the case when the Cartesian set has copies of multiplicative or additive subgroups.

Original language	English
Title of host publication	IEEE International Symposium on Information Theory - Proceedings
Place of Publication	usa
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3160-3165
Number of pages	6
ISBN (Electronic)	9798350382846
DOIs	https://doi.org/10.1109/ISIT57864.2024.10619396
State	Published - Jan 1 2024
Event	2024 IEEE International Symposium on Information Theory, ISIT 2024 - Athens, Greece Duration: Jul 7 2024 → Jul 12 2024

Conference

Conference	2024 IEEE International Symposium on Information Theory, ISIT 2024
Country/Territory	Greece
City	Athens
Period	07/7/24 → 07/12/24

Keywords

Cartesian code
affine transformation
decreasing code
evaluation code
permutation group

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10.1109/ISIT57864.2024.10619396

Cite this

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title = "On the Affine Permutation Group of Certain Decreasing Cartesian Codes",

abstract = "A decreasing Cartesian code is defined by evaluating a monomial set closed under divisibility on a Cartesian set. Some well-known examples are the Reed-Solomon, Reed-Muller, and (some) toric codes. The affine permutations consist of the permutations of the code that depend on an affine transformation. In this work, we study the affine permutations of some decreasing Cartesian codes, including the case when the Cartesian set has copies of multiplicative or additive subgroups.",

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Camps-Moreno, E, López, HH, Sarmiento, E & Soprunov, I 2024, On the Affine Permutation Group of Certain Decreasing Cartesian Codes. in IEEE International Symposium on Information Theory - Proceedings. Institute of Electrical and Electronics Engineers Inc., usa, pp. 3160-3165, 2024 IEEE International Symposium on Information Theory, ISIT 2024, Athens, Greece, 07/7/24. https://doi.org/10.1109/ISIT57864.2024.10619396

On the Affine Permutation Group of Certain Decreasing Cartesian Codes. / Camps-Moreno, Eduardo; López, Hiram H.; Sarmiento, Eliseo et al.
IEEE International Symposium on Information Theory - Proceedings. usa: Institute of Electrical and Electronics Engineers Inc., 2024. p. 3160-3165.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - A decreasing Cartesian code is defined by evaluating a monomial set closed under divisibility on a Cartesian set. Some well-known examples are the Reed-Solomon, Reed-Muller, and (some) toric codes. The affine permutations consist of the permutations of the code that depend on an affine transformation. In this work, we study the affine permutations of some decreasing Cartesian codes, including the case when the Cartesian set has copies of multiplicative or additive subgroups.

AB - A decreasing Cartesian code is defined by evaluating a monomial set closed under divisibility on a Cartesian set. Some well-known examples are the Reed-Solomon, Reed-Muller, and (some) toric codes. The affine permutations consist of the permutations of the code that depend on an affine transformation. In this work, we study the affine permutations of some decreasing Cartesian codes, including the case when the Cartesian set has copies of multiplicative or additive subgroups.

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KW - affine transformation

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KW - evaluation code

KW - permutation group

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On the Affine Permutation Group of Certain Decreasing Cartesian Codes

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Keywords

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