Fooling-sets and rank in nonzero characteristic

  • Mirjam Friesen
  • Dirk Oliver Theis
Part of the CRM Series book series (PSNS, volume 16)


An n × n matrix M is called a fooling-set matrix of size n, if its diagonal entries are nonzero, whereas for every k ≠ ℓ we have Mk,ℓMℓ,k = 0. Dietzfel-binger, Hromkovič, and Schnitger (1996) showed that n ≤ (rkM)2, regardless of over which field the rank is computed, and asked whether the exponent on rkM can be improved.

We settle this question for nonzero characteristic by constructing a family of matrices for which the bound is asymptotically tight. The construction uses linear recurring sequences.


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Copyright information

© Scuola Normale Superiore Pisa 2013

Authors and Affiliations

  • Mirjam Friesen
    • 1
  • Dirk Oliver Theis
    • 2
  1. 1.Faculty of MathematicsOtto von Guericke University MagdeburgGermany
  2. 2.Faculty of Mathematics and Computer ScienceUniversity of TartuEstonia

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