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

Foundation TECNALIA Research & Innovation
University of Oviedo

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

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10.1016/j.disc.2020.111962

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KW - Goppa codes

KW - McEliece cryptosystem

KW - Quaternary codes

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On quaternary Goppa codes

Abstract

Keywords

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