This site uses cookies. By continuing to use this site you agree to our use of cookies. To find out more, see our Privacy and Cookies policy. Close this notification

Properties of sparse random matrices over finite fields

and

Published 24 April 2009 IOP Publishing Ltd
, , Citation Roberto C Alamino and David Saad J. Stat. Mech. (2009) P04017 DOI 10.1088/1742-5468/2009/04/P04017

1742-5468/2009/04/P04017

Abstract

Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.

Export citation and abstract BibTeX RIS

10.1088/1742-5468/2009/04/P04017