A sequence of one-point codes from a tower of function fields

Takehiro Hasegawa, Shoichi Kondo, Hidekazu Kurusu

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    We construct a sequence of one-point codes from a tower of function fields whose relative minimum distances have a positive limit. Our tower is characterized by principal divisors. We determine completely the minimum distance of the codes from the first field of our tower. These results extend those of Stichtenoth [IEEE Trans Inform Theory (1988), 34(15):1345-1348], Yang and Kumar [Lecture Notes in Mathematics, 1518, (1991), Springer-Verlag, Berlin Hidelberg New York, pp. 99-107], and Garcia [Comm. Algebra, 20(12): 3683-3689]. As an application, we show that the minimum distance corresponds to the Feng-Rao bound.

    Original languageEnglish
    Pages (from-to)251-267
    Number of pages17
    JournalDesigns, Codes, and Cryptography
    Volume41
    Issue number3
    DOIs
    Publication statusPublished - 2006 Dec

    Keywords

    • Feng-Rao bound
    • Minimum distance
    • One-point code
    • Tower of function fields

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Theory and Mathematics
    • Applied Mathematics

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