Abstract
We investigate the asymptotic behaviour of the distribution of the number ξ( B ) of the solutions of a system of homogeneous random linear equations Ax = 0 (the T × n matrix A is composed of independent random variables a i , j uniformly distributed on a set of elements of a finite field K ) which belong to some given set B of non-zero n -dimensional vectors over the field K . We consider the case where, under a concordant growth of the parameters n , T → ∞ and variations of the sets B 1 , . . . , B s such that the mean values converge to finite limits, the limit distribution of the vector (ξ( B 1 ), ... , ξ( B s )) is an s -dimensional compound Poisson distribution. We give sufficient conditions for this convergence and find parameters of the limit distribution. We consider in detail the special case where B k is the set of vectors which do not contain a certain element k ∈ K .
Published Version
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