Abstract
Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit oflarge matrices, using techniques from the physics of disordered systems. For the case of a finite fieldGF(q) with primeorder q, we present results for the average kernel dimension, average dimension of the eigenvectorspaces and the distribution of the eigenvalues. The number of matrices for a givendistribution of entries is also calculated for the general case. The significance of theseresults to error-correcting codes and random graphs is also discussed.
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