How to check if elements form a primitive system of a lattice

Question

Given a collection of vectors $V = {v_1, v_2, ..., v_k}$ belonging to a lattice $L$ with basis $B$, is there an efficient procedure that can determine whether or not $V$ forms a primitive system for $L$? This means that if $L$ has rank $n \geq k$, you can extend $V$ by adding $n-k$ vectors such that the resulting set is a basis for $L$.