  In this paper, we present FPT-algorithms for special cases of the shortest
vector problem (SVP) and the integer linear programming problem (ILP), when
matrices included to the problems' formulations are near square. The main
parameter is the maximal absolute value of rank minors of matrices included to
the problem formulation. Additionally, we present FPT-algorithms with respect
to the same main parameter for the problems, when the matrices have no singular
rank sub-matrices.
