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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the generalized Feng-Rao numbers of numerical semigroups generated by intervals


Authors: M. Delgado, J. I. Farrán, P. A. García-Sánchez and D. Llena
Journal: Math. Comp. 82 (2013), 1813-1836
MSC (2010): Primary 20M14, 11Y55, 11T71
Published electronically: January 28, 2013
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Abstract: We give some general results concerning the computation of the generalized Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup generated by an interval, a formula for the $ r^{\mathrm {th}}$ Feng-Rao number is obtained.


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Additional Information

M. Delgado
Affiliation: CMUP, Departamento de Matematica, Faculdade de Ciencias, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Email: mdelgado@fc.up.pt

J. I. Farrán
Affiliation: Departamento de Matemática Aplicada, Escuela Universitaria de Informática, Campus de Segovia - Universidad de Valladolid, Plaza de Santa Eulalia 9 y 11 - 40005 Segovia, Spain
Email: jifarran@eii.uva.es

P. A. García-Sánchez
Affiliation: Departamento de Álgebra, Universidad de Granada, 18071 Granada, España
Email: pedro@ugr.es

D. Llena
Affiliation: Departamento de Geometría, Topología y Química Orgánica, Universidad de Almería, 04120 Almería, España
Email: dllena@ual.es

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02673-7
PII: S 0025-5718(2013)02673-7
Keywords: AG codes, weight hierarchy, numerical semigroups, order bounds, Goppa-like bounds, Feng-Rao numbers.
Received by editor(s): May 19, 2011
Received by editor(s) in revised form: November 22, 2011
Published electronically: January 28, 2013
Additional Notes: The first author was partially funded by the European Regional Development Fund through the program COMPETE and by the Portuguese Government through the FCT - Fundação para a Ciência e a Tecnologia under the project PEst-C/MAT/UI0144/2011.
The second author was supported by the project MICINN-MTM-2007-64704.
The third and fourth authors were supported by the projects MTM2010-15595, FQM-343 and FEDER funds
The third author was also supported by the project FQM-5849.
Article copyright: © Copyright 2013 American Mathematical Society