An invariant for matrices and sets of points in prime characteristic

David Glynn

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    There is polynomial function X q in the entries of an m × m(q - 1) matrix over a field of prime characteristic p, where q = p h is a power of p, that has very similar properties to the determinant of a square matrix. It is invariant under multiplication on the left by a non-singular matrix, and under permutations of the columns. This gives a way to extend the invariant theory of sets of points in projective spaces of prime characteristic, to make visible hidden structure. There are connections with coding theory, permanents, and additive bases of vector spaces.

    Original languageEnglish
    Pages (from-to)155-172
    Number of pages18
    JournalDesigns Codes and Cryptography
    Volume58
    Issue number2
    DOIs
    Publication statusPublished - Feb 2011

    Keywords

    • Additive basis
    • Code
    • Complete weight enumerator
    • Covariant
    • Determinant
    • Invariant
    • P-modular
    • Permanent
    • Prime characteristic
    • Projective geometry

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