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Finding a Vector Orthogonal to Roughly Half a Collection of Vectors

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Abstract

Dimitri Grigoriev has shown that for any family of N vectors in the d-dimensional linear space E = (F_2)^d, there exists a vector in E which is orthogonal to at least N/3 and at most 2N/3 vectors of the family. We show that the range [N/3, 2N/3] can be replaced by the much smaller range [N/2 − √N /2, N/2 + √N /2] and we give an efficient, deterministic parallel algorithm which finds a vector achieving this bound. The optimality of the bound is also investigated.
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Dates and versions

ensl-00153736 , version 1 (11-06-2007)

Identifiers

  • HAL Id : ensl-00153736 , version 1

Cite

Pierre Charbit, Emmanuel Jeandel, Pascal Koiran, Sylvain Perifel, Stéphan Thomassé. Finding a Vector Orthogonal to Roughly Half a Collection of Vectors. 2007. ⟨ensl-00153736⟩
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