Reference request for linear algebra over GF(2)

I have been looking for materials on the linear algebra over $GF(2)$ but so far I haven't found any substantial textbooks or notes on this subject. In fact in one of the notes I found the introduction states that,

Normally, we would cite a series of useful textbooks with background informa- tion but amazingly there is no text for finite field linear algebra. We do not know why this is the case.

In particular I would like to learn about elementary notions such as linear independence, orthogonality, linear equations, rank and kernels, etc. I would especially like to understand what the implications of this properties are when considering the same problem over $\mathbb{R}$. (Eg. does linear independence over $GF(2)$ imply linear independence over $\mathbb{R}$? Does orthogonality over $GF(2)$ imply linear independence over $\mathbb{R}$?)

What are some good notes, textbooks or other sources to learn about this subject?

Asked by user17104 (226 )
Nov 18, 2021 at 03:37