Properties of sparse random matrices over finite fields

Roberto C. Alamino; David Saad

doi:10.1088/1742-5468/2009/04/P04017

Properties of sparse random matrices over finite fields

Roberto C. Alamino, David Saad

Aston University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	P04017
Pages (from-to)	P04017
Journal	Journal of Statistical Mechanics
Volume	2009
Issue number	4
DOIs	https://doi.org/10.1088/1742-5468/2009/04/P04017
Publication status	Published - Apr 2009

Bibliographical note

Copyright of the Institute of Physics

Keywords

random graphs
networks
new applications of statistical mechanics
random matrix theory and extensions

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Properties of sparse random matrices over finite fields

Abstract

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Keywords

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