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Título
On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups
Año del Documento
2018
Editorial
Springer Link
Descripción
Producción Científica
Documento Fuente
Designs, Codes and Cryptography, 2018, vol. 86, n. 12, p. 2893-2916
Resumen
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.
Palabras Clave
Algebraic geometry codes
Código geométrico-algebráico
Feng-Rao distance
Distancia Feng-Rao
Arf semigroups
Semigrupos de Arf
ISSN
1573-7586
Revisión por pares
SI
Patrocinador
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)
Junta de Andalucía (Grant FQM-343)
Fundação para a Ciência e a Tecnologia (Project UID/MAT/00297/2013)
Version del Editor
Propietario de los Derechos
© 2018 Springer
Idioma
eng
Derechos
openAccess
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