Title: The rank of random matrices over finite fields
|Affiliation:||University of Waterloo|
We determine the rank of a random matrix over a finite field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. The proofs are based on the Aizenman-Sims-Starr coupling arguments from mathematical physics.
This work is a collaboration with A. Coja-Oghlan.
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