On minors of maximal determinant matrices

Richard P. Brent, Judy Anne H. Osborn

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    4 Citations (Scopus)

    Abstract

    By an old result of Cohn (1965), a Hadamard matrix of order n has no proper Hadamard submatrix of order m > n/2. We generalize this result to maximal determinant submatrices of Hadamard matrices, and show that an interval of length ~ n/2 is excluded from the allowable orders. We make a conjecture regarding a lower bound for sums of squares of minors of maximal determinant matrices, and give evidence to support it. We give tables of the values taken by the minors of all maximal determinant matrices of orders ≤ 21 and make some observations on the data. Finally, we describe the algorithms that were used to compute the tables.

    Original languageEnglish
    JournalJournal of Integer Sequences
    Volume16
    Issue number4
    Publication statusPublished - 10 Mar 2013

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