Characteristics of random systems of linear equations over a finite field
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A. V. Shapovalov
Abstract
We consider random and a priori consistent random systems of equations over a finite field with q elements in n unknowns. A random system consists of M = M(n) equations, each of which can depend on 2, 3, …, m variables, which are obtained by sampling without replacement. We obtain limit distributions and estimates of moments for the numbers of solutions of random systems of equations provided that n → ∞ and the relation between the parameters n and M, the number of vertices and the number of hyperedges, falls into the subcritical domain of the evolution of random hypergraphs which describe the random systems of equations. The form and parameters of the limit distributions are determined by the characteristics of the limit distributions of the number of cycles of a special form in the corresponding random hypergraphs.
© de Gruyter 2008
Articles in the same Issue
- On stability of a vector combinatorial problem with MINMIN criteria
- On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a random sequence
- Characteristics of random systems of linear equations over a finite field
- On the realisation of Boolean functions by informational graphs
- Estimates of the number of occurrences of vectors on cycles of linear recurring sequences over a finite field
- Finite generability of some groups of recursive permutations
- Independent systems of generators and the Hopf property for unary algebras
- Estimates of the complexity of approximation of continuous functions in some classes of determinate functions with delay
- On ranks, Green classes, and the theory of determinants of Boolean matrices
Articles in the same Issue
- On stability of a vector combinatorial problem with MINMIN criteria
- On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a random sequence
- Characteristics of random systems of linear equations over a finite field
- On the realisation of Boolean functions by informational graphs
- Estimates of the number of occurrences of vectors on cycles of linear recurring sequences over a finite field
- Finite generability of some groups of recursive permutations
- Independent systems of generators and the Hopf property for unary algebras
- Estimates of the complexity of approximation of continuous functions in some classes of determinate functions with delay
- On ranks, Green classes, and the theory of determinants of Boolean matrices
