2024-03-28T22:53:08Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/359382021-09-07T08:33:09Zcom_10324_32197com_10324_952com_10324_894col_10324_32199
On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups
Farrán Martín, José Ignacio
García Sánchez, Pedro A.
Heredia, Benjamín A.
Algebraic geometry codes
Código geométrico-algebráico
Feng-Rao distance
Distancia Feng-Rao
Arf semigroups
Semigrupos de Arf
Producción Científica
We describe the second (generalized) Feng-Rao distance for elements in an Arf numerical semigroup that are greater than or equal to the conductor of the semigroup. This provides a lower bound for the second Hamming weight for one point AG codes. In particular, we can obtain the second Feng-Rao distance for the codes defined by asymptotically good towers of function fields whose Weierstrass semigroups are inductive. In addition, we compute the second Feng-Rao number, and provide some examples and comparisons with previous results on this topic. These calculations rely on Apéry sets, and thus several results concerning Apéry sets of Arf semigroups are presented.
Ministerio de Economía, Industria y Competitividad; y Fondo Europeo de Desarrollo Regional FEDER( Projects MTM2014-55367-P / MTM2015-65764-C3-1-P)
Junta de Andalucía (Grant FQM-343)
Fundação para a Ciência e a Tecnologia (Project UID/MAT/00297/2013)
2019-05-06T12:11:10Z
2019-05-06T12:11:10Z
2018
info:eu-repo/semantics/article
Designs, Codes and Cryptography, 2018, vol. 86, n. 12, p. 2893-2916
1573-7586
http://uvadoc.uva.es/handle/10324/35938
https://doi.org/10.1007/s10623-018-0483-4
eng
https://link.springer.com/article/10.1007%2Fs10623-018-0483-4
Attribution-NonCommercial-NoDerivatives 4.0 International
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
© 2018 Springer
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Springer Link
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Hispana
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http://creativecommons.org/licenses/by-nc-nd/4.0/
UVaDOC. Repositorio Documental de la Universidad de Valladolid
http://uvadoc.uva.es/handle/10324/35938