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

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

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1849-1864
Number of pages16
JournalDesigns, Codes, and Cryptography
Volume86
Issue number8
DOIs
Publication statusPublished - 1 Aug 2018

Keywords

  • AG codes
  • Apéry sets
  • Feng–Rao distances
  • Free Numerical semigroups
  • Generalized Hamming weights
  • Telescopic numerical semigroups

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