ON MINIMAL COSET COVERING OF SOLUTIONS OF A BOOLEAN EQUATION

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ON MINIMAL COSET COVERING OF SOLUTIONS OF A BOOLEAN EQUATION Ashot Minasyan

For the equation x1x2…xn+xn+1xn+2…x2n+x2n+1x2n+2…x3n=1 over the finite field F2 we estimate the minimal number of systems of linear equations over the same field such that the union of their solutions exactly coincides with the set of solutions of the equation. We prove in this article that the number in the question is not greater than 9nlog2⁡3+4.

DOI: 10.46991/PYSUA.2015.49.1.026 Physical and Mathematical Sciences, 49 (1 (236) 26-30

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Keywords

linear algebra, covering with cosets, blocking set

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