Distance bounds for algebraic geometric codes

Iwan Duursma, Radoslav Kirov, Seungkook Park

Research output: Contribution to journalArticlepeer-review

Abstract

Various methods have been used to obtain improvements of the Goppa lower bound for the minimum distance of an algebraic geometric code. The main methods divide into two categories, and all but a few of the known bounds are special cases of either the Lundell-McCullough floor bound or the Beelen order bound. The exceptions are recent improvements of the floor bound by Güneri, Stichtenoth, and Taskin, and by Duursma and Park, and of the order bound by Duursma and Park, and by Duursma and Kirov. In this paper, we provide short proofs for all floor bounds and most order bounds in the setting of the van Lint and Wilson AB method. Moreover, we formulate unifying theorems for order bounds and formulate the DP and DK order bounds as natural but different generalizations of the Feng-Rao bound for one-point codes.

Original languageEnglish (US)
Pages (from-to)1863-1878
Number of pages16
JournalJournal of Pure and Applied Algebra
Volume215
Issue number8
DOIs
StatePublished - Aug 2011

ASJC Scopus subject areas

  • Algebra and Number Theory

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