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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 12/2018

12-04-2018

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

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

Published in: Designs, Codes and Cryptography | Issue 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.
previous article Constructions of complete permutation polynomials
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Metadata
Title
On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups
Authors
José I. Farrán
Pedro A. García-Sánchez
Benjamín A. Heredia
Publication date
12-04-2018
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 12/2018
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-018-0483-4

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