On the duals of geometric Goppa codes from norm-trace curves

Edoardo Ballico, Alberto Ravagnani

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)

Abstract

In this paper we study the dual codes of a wide family of evaluation codes on norm-trace curves. We explicitly find out their minimum distance and give a lower bound for the number of their minimum-weight codewords. A general geometric approach is performed and applied to study in particular the dual codes of one-point and two-point codes arising from norm-trace curves through Goppas construction, providing in many cases their minimum distance and some bounds on the number of their minimum-weight codewords. The results are obtained by showing that the supports of the minimum-weight codewords of the studied codes obey some precise geometric laws as zero-dimensional subschemes of the projective plane. Finally, the dimension of some classical two-point Goppa codes on norm-trace curves is explicitely computed.

Original languageEnglish
Pages (from-to)30-39
Number of pages10
JournalFinite Fields and their Applications
Volume20
Issue number1
DOIs
Publication statusPublished - Mar 2013
Externally publishedYes

Keywords

  • Minimum distance
  • Minimum-weight codeword
  • Norm-trace curve

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