Advances and Applications in Discrete Mathematics
Volume 25, Issue 1, Pages 99 - 111
(September 2020) http://dx.doi.org/10.17654/DM025010099 |
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MATRIX REPRESENTATIONS OF BOOLEAN FUNCTIONS AND THEIR APPLICATION
O. V. Kuzmin and N. A. Gainulin
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Abstract: The work presents an algorithm of construction of a matrix and (1, –1) matrix according the truth table of the Boolean function. The article describes the concept of the Kronecker degree of the matrices. The authors look into the option of using a matrix presentation to prove the different properties of Boolean functions. This presentation is based on the widely known Sylvester-Hadamard matrices. A series of statements and corollaries with proofs are relying on the matrix presentation. In particular, they consider the non-linearity of the Boolean function with fictitious variables. The authors pay attention to the calculation of the non-linearity of the Boolean function. The paper proposes a way of calculating this characteristic, which is based on the representation of the Boolean function in the form of a matrix. It gives an estimate of the required amount of memory required to implement this algorithm. |
Keywords and phrases: Boolean functions, (0.1) matrices, (1, –1) matrices, fictitious variables, non-linearity, bent functions.
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