We know that a boolean vectorial space of dimension n is defined by all posible n-tuples formed by 0 or 1 in each position (note this set is finite), and adding to this set the operations of:
- Multiply by an scalar (also 0 or 1) -> Boolean multiplication to all its components by this scalar.
- Add 2 vectors -> Boolean sum component by component.
When we select a set of m independent vectors (note this can be writen as a boolean matrix nxm where m<=n of rank m) we can see it as the basis of a boolean subspace from the main one of dimension n. This vectorial subspace is formed by all possible linear combinations of its basis (note its size is, of course, also finite).
I am interested in getting any kind of relationship among the size of a boolean vectorial subspace and any parameter that define it (dimension, orthogonality of its vectors,...).
My main issue comes from that I am not really familiar with specific tools to be used in finite vectorial spaces.