RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Guidelines for authors Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Vopr. Kriptogr.: Year: Volume: Issue: Page: Find

 Mat. Vopr. Kriptogr., 2019, Volume 10, Issue 4, Pages 67–76 (Mi mvk308)

On the rank of random binary matrix with fixed weights of independent rows

V. I. Kruglov, V. G. Mikhailov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We consider random matrix consisting of $n$ independent rows such that each row is equiprobably chosen from the set of all $m$-dimensional ($m>n$) binary vectors with given weights $s_i$, $i=1,\ldots,n$, and study asymptotic properties of the rank of such matrix.
We propose explicit upper bound for the distribution function of the rank of matrixes.

Key words: random matrix over $GF(2)$, distribution of the rank of random matrix, upper bound.

DOI: https://doi.org/10.4213/mvk308

Full text: PDF file (177 kB)
First page: PDF file
References: PDF file   HTML file

UDC: 519.212.2

Citation: V. I. Kruglov, V. G. Mikhailov, “On the rank of random binary matrix with fixed weights of independent rows”, Mat. Vopr. Kriptogr., 10:4 (2019), 67–76

Citation in format AMSBIB
\Bibitem{KruMik19} \by V.~I.~Kruglov, V.~G.~Mikhailov \paper On the rank of random binary matrix with fixed weights of independent rows \jour Mat. Vopr. Kriptogr. \yr 2019 \vol 10 \issue 4 \pages 67--76 \mathnet{http://mi.mathnet.ru/mvk308} \crossref{https://doi.org/10.4213/mvk308}