On minors of maximal determinant matrices

Title: On minors of maximal determinant matrices
Creator: Brent, Richard P.; Osborn, Judy-anne H.
Relation: Journal of Integer Sequences Vol. 16, Issue 4
Relation: https://cs.uwaterloo.ca/journals/JIS/
Publisher: University of Waterloo
Resource Type: journal article
Date: 2013
Description: 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.
Subject: Hadamard matrices; maximal determinant matrices; saturated D-optimal designs; minors
Identifier: http://hdl.handle.net/1959.13/1341294
Identifier: uon:28706
Identifier: ISSN:1530-7638
Language: eng
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