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.
That might open the door to more of this kind of thing if you're interested.
A case of proprietary protocols? (Like MPEG?)
galois fields are very interesting for random linear network coding, so of course there is a very thorough patent group (recently sold off, I believe) around it.
given the seriously transformative effects it can have on communications networks -- especially wireless -- I'm both saddened and unsurprised it's in basically nothing as of yet. because it's patented to Hell & Back.