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Proceedings of the Yerevan State University, series Physical and Mathematical Sciences, 2015, Issue 1, Pages 26–30
(Mi uzeru9)
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This article is cited in 1 scientific paper (total in 1 paper)
Mathematics
On minimal coset covering of solutions of a boolean equation
A. V. Minasyan Yerevan State University
Abstract:
For the equation $x_1x_2\dots x_n+x_{n+1}x_{n+2}\dots x_{2n}+x_{2n+1}x_{2n+2}\dots x_{3n}=1$ over
the finite field $F_2$ 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 $9n^{\log_2^3}+4.$
Keywords:
linear algebra, covering with cosets, blocking set.
Received: 22.01.2015 Accepted: 12.02.2015
Citation:
A. V. Minasyan, “On minimal coset covering of solutions of a boolean equation”, Proceedings of the YSU, Physical and Mathematical Sciences, 2015, no. 1, 26–30
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https://www.mathnet.ru/eng/uzeru9 https://www.mathnet.ru/eng/uzeru/y2015/i1/p26
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