A condition for arcs and MDS codes

David Glynn

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    A set of n + k points (k > 0) in projective space of dimension n is said to be an (n + k)-arc if there is no hyperplane containing any n + 1 points of the set. It is well-known that for the projective space PG(n, q), this is equivalent to a maximum distance separable linear code with symbols in the finite field GF(q), of length n + k, dimension n + 1, and distance d = k that satisfies the Singleton bound d ≤ k. We give an algebraic condition for such a code, or set of points, and this is associated with an identity involving determinants.

    Original languageEnglish
    Pages (from-to)215-218
    Number of pages4
    JournalDesigns Codes and Cryptography
    Volume58
    Issue number2
    DOIs
    Publication statusPublished - Feb 2011

    Keywords

    • Arc
    • Determinant
    • General position
    • Grassmannian
    • MDS code
    • Projective space

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