I have vectors in such form
(1 1 1 0 1 0) (0 0 1 0 0 0) (1 0 0 0 0 0) (0 0 0 1 0 0) (1 1 0 0 1 0) (0 0 1 1 0 0) (1 0 1 1 0 0)
I need to find all linear dependent subsets over $Z_2$.
For example 1,2,5 and 3,6,7.
EDIT (after @rschwieb)
The answer for presented vectors: 521 642 763 6541 7432 75431 765321
I did by brute force. I mean i wrote program to iterate through all variants in ${7 \choose 3} {7 \choose 4} {7 \choose 5} {7 \choose 6} {7 \choose 7}$ 99 in total.
But i just thought what some method exist for such task. For now im trying to implement http://en.wikipedia.org/wiki/Quadratic_sieve . Code incorporated in whole program. I plan to put it here then i organize it well.