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arXiv · 1208.1805

General lower bounds on maximal determinants of binary matrices

Richard P. Brent·Judy-anne H. Osborn
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Abstract

We give general lower bounds on the maximal determinant of n by n {+1,-1}-matrices, both with and without the assumption of the Hadamard conjecture. Our bounds improve on earlier results of de Launey and Levin (2010) and, for certain congruence classes of n mod 4, those of Koukouvinos, Mitrouli and Seberry (2000). In an Appendix we give a new proof, using Jacobi's determinant identity, of a result of Szöllősi (2010) on minors of Hadamard matrices.

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Richard P. Brent, Judy-anne H. Osborn. 2013-04-14. General lower bounds on maximal determinants of binary matrices. https://doi.org/10.37236/2612

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