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Erschienen in: Designs, Codes and Cryptography 12/2018

12.04.2018

On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups

verfasst von: José I. Farrán, Pedro A. García-Sánchez, Benjamín A. Heredia

Erschienen in: Designs, Codes and Cryptography | Ausgabe 12/2018

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Abstract

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.
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Metadaten
Titel
On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups
verfasst von
José I. Farrán
Pedro A. García-Sánchez
Benjamín A. Heredia
Publikationsdatum
12.04.2018
Verlag
Springer US
Erschienen in
Designs, Codes and Cryptography / Ausgabe 12/2018
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-018-0483-4

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