Starting here:
http://www.eccpage.com/rs.c
You can pre-compute alpha_to, index_of, and gg
For the case in the example program that is 16+16+7 ints (do they need to be ints or will bytes work?) or 156 bytes
That example has 9 ints of data and 6 ints of ecc or 15 total, if these are 4 byte ints that is another 60 bytes, 216 total.
Or 54 bytes if this could be done with bytes only. I seem to remember it works with bytes.
The encoder routine itself has a modulo but you can probably replace that with an and depending on your lengths. If your embedded processor has a divide then that is probably not going to hurt you anyway. Otherwise the encoder routine is quite simple. I am thinking that you may approach 500 bytes with the tables, data, and code.
I dont remember how to get from the 9 data and 6 ecc of the example to the 10 and 5 you are looking for. Hopefully the code in the link above will give you a head start to what you are looking for.