Good that this is more on the practical side, i.e. talking about bits and bytes instead of just abstract numerical theory. It really helps when learning this stuff --- a while ago I was reading about Reed-Solomon (which also uses GF) and I could find plenty of theoretical material, but there was a noticeable shortage of practical implementation-oriented detail.
Oh just be careful one of the early seminal "how to implement" papers has an incorrect description of the vandermonde matrix which results in not being able to guarantee matrix inversions. Be sure to check the errata for older papers.
If you want a good "halfway between theory and practice" experience, I suggest implementing gf256 in Julia. That is, create the datatype and define +, -, *, /. (Along the way g^n and log_g might be helpful too). For Julia > 0.6.2 the builtin lu factorization operator is general enough that once you've definitely the basic 4 operations (and zero(gf256) and one(gf256)) you can call the matrix solve operation \ on your datatype and immediately recover your erasures without having to go through tedious coding of an elimination routine.
The translation is actually pretty automatic once you get used to it. One way to get a handle on the more abstract language is by looking at me elementary number theory stuff and manually translating it to the bits and bytes language yourself.
That might open the door to more of this kind of thing if you're interested.
