Difference between $F_2^n$ and $\Bbb F_2^n$ for a field I am confused between the notation $F_2^n$ and $\Bbb F_2^n$ for a field in regards to codes. 

I thought that $F_2^n$ and $\Bbb F_2^n$ were both fields composed by codes of length n and entries in mod 2, but I now know that this cannot be true.
What is the difference between them?

For example, if code C is consists of all the codewords in $F_n^2$ that have even weight, to show that C is a linear code, do I use the fact that it is a subspace of $F_2^n$ or $\Bbb F_2^n$?

Thank you!
Some authors write $F_q$ for the finite field of order $q$.  Some authors write $\mathbb F_q$.  Some authors write $\mathbf F_q$.  Unless there's a typo, or unless your pet author is particularly confusing and as a personal peculiarity makes a nonstandard semantic distinction between them, which one you use is a matter of taste.  And as we all know—de gustibus non disputandum est: only with gusto can taste be argued.

What parts of the text you are reading are leading you to a state of confusion?  Maybe you can ask a question about those in particular.