On quaternary Goppa codes

Markel Epelde; Xabier Larrucea; Ignacio F. Rúa

doi:10.1016/j.disc.2020.111962

On quaternary Goppa codes

Markel Epelde, Xabier Larrucea, Ignacio F. Rúa

Tecnalia Research & Innovation

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In Goppa (1970), V. D. Goppa presents a new family of linear codes over finite fields. This family, now known as Goppa codes, has been studied for nearly 50 years, including efficient decoding algorithms (Patterson, 1975) and its applications in cryptography (McEliece, 1978). Moreover, in Andrade et al. (2005), de Andrade and Palazzo present a generalization of Goppa codes to finite rings. Motivated by cryptographic applications, in this article we focus on Goppa codes over Z∕4Z and study some of their properties.

Original language	English
Article number	111962
Journal	Discrete Mathematics
Volume	343
Issue number	9
DOIs	https://doi.org/10.1016/j.disc.2020.111962
Publication status	Published - Sept 2020

Keywords

Goppa codes
McEliece cryptosystem
Quaternary codes

Access to Document

10.1016/j.disc.2020.111962

Cite this

@article{bbea573537e045f4b66c55ffc3309e81,

title = "On quaternary Goppa codes",

abstract = "In Goppa (1970), V. D. Goppa presents a new family of linear codes over finite fields. This family, now known as Goppa codes, has been studied for nearly 50 years, including efficient decoding algorithms (Patterson, 1975) and its applications in cryptography (McEliece, 1978). Moreover, in Andrade et al. (2005), de Andrade and Palazzo present a generalization of Goppa codes to finite rings. Motivated by cryptographic applications, in this article we focus on Goppa codes over Z∕4Z and study some of their properties.",

keywords = "Goppa codes, McEliece cryptosystem, Quaternary codes",

author = "Markel Epelde and Xabier Larrucea and R{\'u}a, {Ignacio F.}",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2020",

month = sep,

doi = "10.1016/j.disc.2020.111962",

language = "English",

volume = "343",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "9",

}

TY - JOUR

T1 - On quaternary Goppa codes

AU - Epelde, Markel

AU - Larrucea, Xabier

AU - Rúa, Ignacio F.

PY - 2020/9

Y1 - 2020/9

N2 - In Goppa (1970), V. D. Goppa presents a new family of linear codes over finite fields. This family, now known as Goppa codes, has been studied for nearly 50 years, including efficient decoding algorithms (Patterson, 1975) and its applications in cryptography (McEliece, 1978). Moreover, in Andrade et al. (2005), de Andrade and Palazzo present a generalization of Goppa codes to finite rings. Motivated by cryptographic applications, in this article we focus on Goppa codes over Z∕4Z and study some of their properties.

AB - In Goppa (1970), V. D. Goppa presents a new family of linear codes over finite fields. This family, now known as Goppa codes, has been studied for nearly 50 years, including efficient decoding algorithms (Patterson, 1975) and its applications in cryptography (McEliece, 1978). Moreover, in Andrade et al. (2005), de Andrade and Palazzo present a generalization of Goppa codes to finite rings. Motivated by cryptographic applications, in this article we focus on Goppa codes over Z∕4Z and study some of their properties.

KW - Goppa codes

KW - McEliece cryptosystem

KW - Quaternary codes

UR - http://www.scopus.com/inward/record.url?scp=85084738227&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2020.111962

DO - 10.1016/j.disc.2020.111962

M3 - Article

AN - SCOPUS:85084738227

SN - 0012-365X

VL - 343

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 9

M1 - 111962

ER -

On quaternary Goppa codes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this