The minimum weights of two-point AG codes on norm-trace curves

Boran Kim, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We construct two-point algebraic geometry codes (AG codes) on algebraic curves over a finite field. We find the order-like bound on the minimum weights of these codes on algebraic curves, and we prove that this order-like bound is better than the Goppa bound. On norm-trace curves over the finite fields of characteristic 2, we explicitly determine the order-like bounds for one-point AG codes and two-point AG codes. Consequently, it turns out that the order-like bound for two-point AG codes on norm-trace curves is better than that of one-point codes on the same curves except for a few cases.

Original languageEnglish
Pages (from-to)113-139
Number of pages27
JournalFinite Fields and their Applications
Volume53
DOIs
StatePublished - Sep 2018

Bibliographical note

Publisher Copyright:
© 2018

Keywords

  • AG codes
  • Algebraic geometry codes
  • Minimum weights
  • Norm-trace curves
  • The order bound

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