An Extension of the Order Bound for AG Codes

Iwan M Duursma, Radoslav Kirov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The most successful method to obtain lower bounds for the minimum distance of an algebraic geometric code is the order bound, which generalizes the Feng-Rao bound. By using a finer partition of the set of all codewords of a code we improve the order bounds by Beelen and by Duursma and Park. We show that the new bound can be efficiently optimized and we include a numerical comparison of different bounds for all two-point codes with Goppa distance between 0 and 2g∈-∈1 for the Suzuki curve of genus g∈=∈124 over the field of 32 elements.

Original languageEnglish (US)
Title of host publicationApplied Algebra, Algebraic Algorithms, and Error-Correcting Codes - 18th International Symposium, AAECC-18, Proceedings
Pages11-22
Number of pages12
DOIs
StatePublished - Aug 21 2009
Event18th International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, AAECC-18 - Tarragona, Spain
Duration: Jun 8 2009Jun 12 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5527 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other18th International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, AAECC-18
CountrySpain
CityTarragona
Period6/8/096/12/09

Keywords

  • Algebraic geometric code
  • Order bound
  • Suzuki curve

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Duursma, I. M., & Kirov, R. (2009). An Extension of the Order Bound for AG Codes. In Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes - 18th International Symposium, AAECC-18, Proceedings (pp. 11-22). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5527 LNCS). https://doi.org/10.1007/978-3-642-02181-7_2