On certain self-orthogonal AG codes with applications to Quantum error-correcting codes

Daniele Bartoli; Maria Montanucci; Giovanni Zini

doi:10.1007/s10623-021-00870-y

On certain self-orthogonal AG codes with applications to Quantum error-correcting codes

Daniele Bartoli, Maria Montanucci, Giovanni Zini^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss curves. Several classes of well-known algebraic curves with many rational points turn out to be Swiss curves. Examples are given by Castle curves, GK curves, generalized GK curves and the Abdón–Bezerra–Quoos maximal curves. Applications of our method to these curves are provided. Our construction extends a previous one due to Hernando, McGuire, Monserrat, and Moyano-Fernández.

Original language	English
Journal	Designs, Codes, and Cryptography
Volume	13
Pages (from-to)	1-19
ISSN	0925-1022
DOIs	https://doi.org/10.1007/s10623-021-00870-y
Publication status	Published - 2021

Keywords

Finite fields
Algebraic geometry codes
Quantum error-correction
Algebraic curves

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title = "On certain self-orthogonal AG codes with applications to Quantum error-correcting codes",

abstract = "In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss curves. Several classes of well-known algebraic curves with many rational points turn out to be Swiss curves. Examples are given by Castle curves, GK curves, generalized GK curves and the Abd{\'o}n–Bezerra–Quoos maximal curves. Applications of our method to these curves are provided. Our construction extends a previous one due to Hernando, McGuire, Monserrat, and Moyano-Fern{\'a}ndez.",

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AU - Bartoli, Daniele

AU - Montanucci, Maria

AU - Zini, Giovanni

PY - 2021

Y1 - 2021

N2 - In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss curves. Several classes of well-known algebraic curves with many rational points turn out to be Swiss curves. Examples are given by Castle curves, GK curves, generalized GK curves and the Abdón–Bezerra–Quoos maximal curves. Applications of our method to these curves are provided. Our construction extends a previous one due to Hernando, McGuire, Monserrat, and Moyano-Fernández.

AB - In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss curves. Several classes of well-known algebraic curves with many rational points turn out to be Swiss curves. Examples are given by Castle curves, GK curves, generalized GK curves and the Abdón–Bezerra–Quoos maximal curves. Applications of our method to these curves are provided. Our construction extends a previous one due to Hernando, McGuire, Monserrat, and Moyano-Fernández.

KW - Finite fields

KW - Algebraic geometry codes

KW - Quantum error-correction

KW - Algebraic curves

U2 - 10.1007/s10623-021-00870-y

DO - 10.1007/s10623-021-00870-y

M3 - Journal article

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VL - 13

SP - 1

EP - 19

JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

ER -

On certain self-orthogonal AG codes with applications to Quantum error-correcting codes

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Keywords

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