Motivated by a connection with block iterative methods for solving linear systems over finite fields, we consider the probability that the Krylov space generated by a fixed linear mapping and a random set of elements in a vector space over a finite field equals the space itself. We obtain an exact formula for this probability, and from it we derive good lower bounds that approach 1 exponentially fast as the size of the set increases.
We define a random sequence of reals as a random point on a computable topological space. This rando...
Let $A$ be a random $m\times n$ matrix over the finite field $F_q$ with precisely $k$ non-zero entri...
Let f be a uniformly random element of the set of all mappings from [n] = {1, ..., n} to itself. Let...
Motivated by a connection with block iterative methods for solving linear systems over finite fields...
This paper deals with the probability of classical system-theoretic properties of random linear syst...
Motivated by the problem of finding light (i.e., low weight) and short (i.e., low degree) codewords ...
. We improve on a lattice algorithm of Tezuka for the computation of the k-distribution of a class o...
This paper deals with the probability that random linear systems defined over a finite field are rea...
Let f be a uniformly random element of the set of all mappings from [n] = {1,... , n} to itself. Let...
Abstract. The first part of this paper surveys generating functions methods in the study of random m...
We extend the "method of multiplicities" to get the following results, of interest in combinatorics ...
AbstractThe aim of the paper is to compile and compare basic theoretical facts on Krylov subspaces a...
For various random constraint satisfaction problems there is a significant gap between the largest c...
A Kakeya, or Besicovitch, set in a vector space is a set which contains a line in every direction. T...
textabstractWe study the set of incompressible strings for various resource bounded versions of Kolm...
We define a random sequence of reals as a random point on a computable topological space. This rando...
Let $A$ be a random $m\times n$ matrix over the finite field $F_q$ with precisely $k$ non-zero entri...
Let f be a uniformly random element of the set of all mappings from [n] = {1, ..., n} to itself. Let...
Motivated by a connection with block iterative methods for solving linear systems over finite fields...
This paper deals with the probability of classical system-theoretic properties of random linear syst...
Motivated by the problem of finding light (i.e., low weight) and short (i.e., low degree) codewords ...
. We improve on a lattice algorithm of Tezuka for the computation of the k-distribution of a class o...
This paper deals with the probability that random linear systems defined over a finite field are rea...
Let f be a uniformly random element of the set of all mappings from [n] = {1,... , n} to itself. Let...
Abstract. The first part of this paper surveys generating functions methods in the study of random m...
We extend the "method of multiplicities" to get the following results, of interest in combinatorics ...
AbstractThe aim of the paper is to compile and compare basic theoretical facts on Krylov subspaces a...
For various random constraint satisfaction problems there is a significant gap between the largest c...
A Kakeya, or Besicovitch, set in a vector space is a set which contains a line in every direction. T...
textabstractWe study the set of incompressible strings for various resource bounded versions of Kolm...
We define a random sequence of reals as a random point on a computable topological space. This rando...
Let $A$ be a random $m\times n$ matrix over the finite field $F_q$ with precisely $k$ non-zero entri...
Let f be a uniformly random element of the set of all mappings from [n] = {1, ..., n} to itself. Let...
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