TY - JOUR
T1 - On quaternary Goppa codes
AU - Epelde, Markel
AU - Larrucea, Xabier
AU - Rúa, Ignacio F.
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
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 -