Rank and kernel of binary Hadamard codes

Kevin T. Phelps, Josep Rifà, Mercè Villanueva

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    15 Citations (Scopus)

    Abstract

    In this paper, the rank and the dimension of the kernel for (binary) Hadamard codes of length a power of two are studied. In general, it is well-known that the rank of a Hadamard code of length n = 2t is a value in {t+1,..., n/2}. In the present paper, the range of possible values for the dimension of the kernel is computed and a construction of Hadamard codes of length n = 2t for each one of these values is given. Lower and upper bounds for the rank and dimension of the kernel of a Hadamard code of length n = 2t are also established. Finally, we construct Hadamard codes for all possible ranks and dimension of kernels between these bounds. © 2005 IEEE.
    Original languageEnglish
    Pages (from-to)3931-3937
    JournalIEEE Transactions on Information Theory
    Volume51
    DOIs
    Publication statusPublished - 1 Nov 2005

    Keywords

    • Extended perfect codes
    • Hadamard codes
    • Hadamard matrices
    • Kernel
    • Rank

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