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Non-asymptotic bounds for probabilities of the rank of a random matrix over a finite field
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A. N. Alekseychuk
Published/Copyright:
June 28, 2007
We consider a random (n + s) × n matrix A with independent rows over a field of q elements. In terms of the Fourier coefficients of distributions of the rows of this matrix we obtain expressions of upper and (in the case where the Fourier coefficients are non-negative quantities) lower bounds for probabilities of values of its rank. We find an upper bound for the distance in variation between the distributions of ranks of the matrix A and a random equiprobable matrix. We present a condition for this distance to tend to zero as 
and s is fixed and demonstrate that this condition, in some natural sense, cannot be weakened.
Published Online: 2007-06-28
Published in Print: 2007-07-20
Copyright 2007, Walter de Gruyter
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