I have vectors $v_i$ such that $1\leq i \leq m $ of dimension $n$ where $m > n$. Members of the vectors $v$ belongs to $GF(2^k)$ (hope it makes it easier).
Ideally, all these vectors should be in the same vectorspace formed by any $n$ of these vectors. But in my problem there are few vectors that doesn't belong to the vector space.
$m$ and $n$ are usually in the range of 40 and 20 which results in a big combination of $n$ elements out of $m$ that I think isn't practical to traverse all of these combinations !!