An Extension of the Order Bound for AG Codes

Iwan Duursma; Radoslav Kirov

doi:10.1007/978-3-642-02181-7_2

An Extension of the Order Bound for AG Codes

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes - 18th International Symposium, AAECC-18, Proceedings
Pages	11-22
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-02181-7_2
State	Published - 2009
Event	18th International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, AAECC-18 - Tarragona, Spain Duration: Jun 8 2009 → Jun 12 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5527 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	18th International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, AAECC-18
Country/Territory	Spain
City	Tarragona
Period	6/8/09 → 6/12/09

Keywords

Algebraic geometric code
Order bound
Suzuki curve

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Online availability

10.1007/978-3-642-02181-7_2

Library availability

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Cite this

Duursma, I., & 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

An Extension of the Order Bound for AG Codes. / Duursma, Iwan; Kirov, Radoslav.
Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes - 18th International Symposium, AAECC-18, Proceedings. 2009. p. 11-22 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5527 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Duursma, I & 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. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5527 LNCS, pp. 11-22, 18th International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, AAECC-18, Tarragona, Spain, 6/8/09. https://doi.org/10.1007/978-3-642-02181-7_2

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

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An Extension of the Order Bound for AG Codes

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