AG codes from the second generalization of the GK maximal curve

Maria Montanucci, Vincenzo Pallozzi Lavorante*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Let q be a prime-power, and n≥3 an odd integer. We determine the structure of the Weierstrass semigroup H(P) where P is an arbitrary Fq2 -rational point of GK2,n where GK2,n stands for the Fq2n -maximal curve of Beelen and Montanucci. We prove that these points are Weierstrass points, and we compute the Frobenius dimension of GK2,n. Using these results, we also show that GK2,n is isomorphic to the Güneri–Garcìa–Stichtenoth only for n=3. Furthermore, AG codes and AG quantum codes from the GK2,n are constructed and discussed. In some cases, they have better parameters compared with those of the known linear codes.

Original languageEnglish
Article number111810
JournalDiscrete Mathematics
Volume243
Issue number5
ISSN0012-365X
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • Algebraic–geometric codes
  • Maximal curves
  • Weierstrass semigroups

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