Computational results on invertible matrices with the maximum number of invertible 2×2 submatrices
نویسندگان
چکیده
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.
منابع مشابه
Invertible binary matrices with maximum number of 2-by-2 invertible submatrices
The problem is related to all-or-nothing transforms (AONT) suggested by Rivest as a preprocessing for encrypting data with a block cipher. Since then there have been various applications of AONTs in cryptography and security. D’Arco, Esfahani and Stinson posed the problem on the constructions of binary matrices for which the desired properties of an AONT hold with the maximum probability. That ...
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 69 شماره
صفحات -
تاریخ انتشار 2017