Minimum weight codewords in dual algebraic-geometric codes from the Giulietti-Korchmáros curve

Daniele Bartoli; Matteo Bonini

doi:10.1007/s10623-018-0541-y

Minimum weight codewords in dual algebraic-geometric codes from the Giulietti-Korchmáros curve

Daniele Bartoli, Matteo Bonini^*

^*Kontaktforfatter

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

6 Citationer (Scopus)

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Abstract

In this paper we investigate the number of minimum weight codewords of some dual algebraic-geometric codes associated with the Giulietti–Korchmáros maximal curve, by computing the maximal number of intersections between the Giulietti–Korchmáros curve and lines, plane conics, and plane cubics.

Originalsprog	Engelsk
Tidsskrift	Designs, Codes, and Cryptography
Vol/bind	87
Udgave nummer	6
Sider (fra-til)	1433-1445
Antal sider	13
ISSN	0925-1022
DOI	https://doi.org/10.1007/s10623-018-0541-y
Status	Udgivet - 15 jun. 2019
Udgivet eksternt	Ja

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© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

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10.1007/s10623-018-0541-y

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title = "Minimum weight codewords in dual algebraic-geometric codes from the Giulietti-Korchm{\'a}ros curve",

abstract = "In this paper we investigate the number of minimum weight codewords of some dual algebraic-geometric codes associated with the Giulietti–Korchm{\'a}ros maximal curve, by computing the maximal number of intersections between the Giulietti–Korchm{\'a}ros curve and lines, plane conics, and plane cubics.",

keywords = "Algebraic-geometric codes, Giulietti–Korchm{\'a}ros curve, Weight distribution",

author = "Daniele Bartoli and Matteo Bonini",

note = "Funding Information: Acknowledgements This research was partially supported by Ministry for Education, University and Research of Italy (MIUR) (Project PRIN 2012 “Geometrie di Galois e strutture di incidenza”—Prot. N. 2012XZE22K−005) and by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA—INdAM). D. Bartoli carried out this research within the project “Progetto Codici correttori di errori”, supported by Fondo Ricerca di Base, 2015, of Universit{\`a} degli Studi di Perugia. M. Bonini would like to thank his supervisor, Massimiliano Sala, for the helpful suggestions. The authors would like to thank the anonymous referees for their helpful and constructive comments that contributed to improve the final version of the paper. Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2019",

month = jun,

day = "15",

doi = "10.1007/s10623-018-0541-y",

language = "English",

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T1 - Minimum weight codewords in dual algebraic-geometric codes from the Giulietti-Korchmáros curve

AU - Bartoli, Daniele

AU - Bonini, Matteo

N1 - Funding Information: Acknowledgements This research was partially supported by Ministry for Education, University and Research of Italy (MIUR) (Project PRIN 2012 “Geometrie di Galois e strutture di incidenza”—Prot. N. 2012XZE22K−005) and by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA—INdAM). D. Bartoli carried out this research within the project “Progetto Codici correttori di errori”, supported by Fondo Ricerca di Base, 2015, of Università degli Studi di Perugia. M. Bonini would like to thank his supervisor, Massimiliano Sala, for the helpful suggestions. The authors would like to thank the anonymous referees for their helpful and constructive comments that contributed to improve the final version of the paper. Publisher Copyright: © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2019/6/15

Y1 - 2019/6/15

N2 - In this paper we investigate the number of minimum weight codewords of some dual algebraic-geometric codes associated with the Giulietti–Korchmáros maximal curve, by computing the maximal number of intersections between the Giulietti–Korchmáros curve and lines, plane conics, and plane cubics.

AB - In this paper we investigate the number of minimum weight codewords of some dual algebraic-geometric codes associated with the Giulietti–Korchmáros maximal curve, by computing the maximal number of intersections between the Giulietti–Korchmáros curve and lines, plane conics, and plane cubics.

KW - Algebraic-geometric codes

KW - Giulietti–Korchmáros curve

KW - Weight distribution

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U2 - 10.1007/s10623-018-0541-y

DO - 10.1007/s10623-018-0541-y

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SN - 0925-1022

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EP - 1445

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

IS - 6

ER -

Minimum weight codewords in dual algebraic-geometric codes from the Giulietti-Korchmáros curve

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