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

Fundación TECNALIA Research & Innovation
University of Oviedo

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

2 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Número de artículo	111962
Publicación	Discrete Mathematics
Volumen	343
N.º	9
DOI	https://doi.org/10.1016/j.disc.2020.111962
Estado	Publicada - sept 2020

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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.",

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KW - McEliece cryptosystem

KW - Quaternary codes

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On quaternary Goppa codes

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