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 Mat. Vopr. Kriptogr., 2020, Volume 11, Issue 3, Pages 41–52 (Mi mvk331)

On the rank of random matrix over prime field consisting of independent rows with given numbers of nonzero elements

V. I. Kruglov, V. G. Mikhailov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: In a recent paper we had proposed explicit bound for the distribution function of the rank of matrix with independent rows having fixed weights. Here this bound is generalized for a wider class of binary matrices with independent rows and also to matrices over prime field ${GF}(p)$ that consist of independent rows, which are chosen from sets of vectors with given numbers of non-zero elements.

Key words: random matrix over $GF(p)$, distribution of rank of a random matrix, explicit bound.

DOI: https://doi.org/10.4213/mvk331

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UDC: 519.212.2

Citation: V. I. Kruglov, V. G. Mikhailov, “On the rank of random matrix over prime field consisting of independent rows with given numbers of nonzero elements”, Mat. Vopr. Kriptogr., 11:3 (2020), 41–52

Citation in format AMSBIB
\Bibitem{KruMik20} \by V.~I.~Kruglov, V.~G.~Mikhailov \paper On the rank of random matrix over prime field consisting of independent rows with given numbers of nonzero elements \jour Mat. Vopr. Kriptogr. \yr 2020 \vol 11 \issue 3 \pages 41--52 \mathnet{http://mi.mathnet.ru/mvk331} \crossref{https://doi.org/10.4213/mvk331}