Rank properties of subspaces of symmetric and Hermitian matrices over finite fields

Abstract : We investigate constant rank subspaces of symmetric and Hermitian matrices over finite fields, using a double counting method related to the number of common zeros of the corresponding subspaces of symmetric bilinear and Hermitian forms. We obtain optimal bounds for the dimensions of constant rank subspaces of Hermitian matrices, and good bounds for the dimensions of subspaces of symmetric and Hermitian matrices whose non-zero elements all have odd rank.
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https://hal.archives-ouvertes.fr/hal-00699691
Contributor : Jean-Guillaume Dumas <>
Submitted on : Monday, May 21, 2012 - 2:39:59 PM
Last modification on : Thursday, July 4, 2019 - 9:54:02 AM

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Jean-Guillaume Dumas, Rod Gow, John Sheekey. Rank properties of subspaces of symmetric and Hermitian matrices over finite fields. Finite Fields and Their Applications, Elsevier, 2011, 17 (6), pp.504-520. ⟨10.1016/j.ffa.2011.03.001⟩. ⟨hal-00699691⟩

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