Duals of Affine Grassmann Codes and Their Relatives

P. Beelen, S. R. Ghorpade, T. Hoholdt

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    Abstract

    Affine Grassmann codes are a variant of generalized Reed-Muller codes and are closely related to Grassmann codes. These codes were introduced in a recent work by Beelen Here, we consider, more generally, affine Grassmann codes of a given level. We explicitly determine the dual of an affine Grassmann code of any level and compute its minimum distance. Further, we ameliorate the results by Beelen concerning the automorphism group of affine Grassmann codes. Finally, we prove that affine Grassmann codes and their duals have the property that they are linear codes generated by their minimum-weight codewords. This provides a clean analogue of a corresponding result for generalized Reed-Muller codes.
    Original languageEnglish
    JournalI E E E Transactions on Information Theory
    Volume58
    Issue number6
    Pages (from-to)3843-3855
    ISSN0018-9448
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Linear codes
    • Reed-Muller codes
    • Electronic mail
    • Frequency modulation
    • Linear code
    • Parity check codes
    • Polynomials
    • Sparse matrices

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