  This paper deals with the computation of the rank and of some integer Smith
forms of a series of sparse matrices arising in algebraic K-theory. The number
of non zero entries in the considered matrices ranges from 8 to 37 millions.
The largest rank computation took more than 35 days on 50 processors. We report
on the actual algorithms we used to build the matrices, their link to the
motivic cohomology and the linear algebra and parallelizations required to
perform such huge computations. In particular, these results are part of the
first computation of the cohomology of the linear group GL_7(Z).
