RT info:eu-repo/semantics/article
T1 On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups
A1 Farrán Martín, José Ignacio
A1 García Sánchez, Pedro A.
A1 Heredia, Benjamín A.
K1 Algebraic geometry codes
K1 Código geométrico-algebráico
K1 Feng-Rao distance
K1 Distancia Feng-Rao
K1 Arf semigroups
K1 Semigrupos de Arf
AB 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.
PB Springer Link
SN 1573-7586
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/35938
UL http://uvadoc.uva.es/handle/10324/35938
LA eng
NO Designs, Codes and Cryptography, 2018, vol. 86, n. 12, p. 2893-2916
NO Producción Científica
DS UVaDOC
RD 24-nov-2024