  Random linear systems over the Galois Field modulo 2 have an interest in
connection with problems ranging from computational optimization to complex
networks. They are often approached using random matrices with
Poisson-distributed or finite column/row-sums. This technical note considers
the typical rank of random matrices belonging to a specific ensemble wich has
genuinely power-law distributed column-sums. For this ensemble, we find a
formula for calculating the typical rank in the limit of large matrices as a
function of the power-law exponent and the shape of the matrix, and
characterize its behavior through "phase diagrams" with varying model
parameters.
