Properties of sparse random matrices over finite fields

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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 languageEnglish
Article numberP04017
Pages (from-to)P04017
JournalJournal of Statistical Mechanics
Volume2009
Issue number4
DOIs
Publication statusPublished - 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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