The second Feng–Rao number for codes coming from telescopic semigroups View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-10-25

AUTHORS

José I. Farrán, Pedro A. García-Sánchez, Benjamín A. Heredia, Micah J. Leamer

ABSTRACT

In this manuscript we show that the second Feng–Rao number of any telescopic numerical semigroup agrees with the multiplicity of the semigroup. To achieve this result we first study the behavior of Apéry sets under gluings of numerical semigroups. These results provide a bound for the second Hamming weight of one-point Algebraic Geometry codes, which improves upon other estimates such as the Griesmer Order Bound. More... »

PAGES

1849-1864

References to SciGraph publications

  • 2013-04-05. Constructing the set of complete intersection numerical semigroups with a given Frobenius number in APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
  • 2012-03-08. Generalized Hermitian codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1997-09-01. On Presentations of Subsemigroups of {\blackboard N}^n in SEMIGROUP FORUM
  • 2009. Numerical Semigroups in NONE
  • 1999. Introduction to Coding Theory in NONE
  • 2016. Numerical Semigroups and Applications in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10623-017-0426-5

    DOI

    http://dx.doi.org/10.1007/s10623-017-0426-5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1092353568


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