论文信息 - Computational results on invertible matrices with the maximum number of invertible 2×2 submatrices

Computational results on invertible matrices with the maximum number of invertible 2×2 submatrices

A linear 2-All-or-Nothing Transform can be considered as an invertible matrix with all 2 × 2 submatrices invertible. It is known [P. D’Arco, N. Nasr Esfahani and D.R. Stinson, Electron. J. Combin. 23(4) (2016), #P4.10] that there is no binary s×s matrix that satisfies these conditions, for s > 2. In this paper, different computational methods for generating invertible binary matrices with close to the maximum number of invertible 2 × 2 submatrices have been implemented and compared against each other. We also study the ternary matrices with such properties.

Douglas R. Stinson | Navid Nasr Esfahani

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