"I don't have much time [...]. What do you recommend that I do?"
Set Specific Goals. Your goal must be clear and well defined.
- Chose a small, a medium and a large picture.
- Your computer system
- Set acceptable execution times, number of seconds, for encoding and decoding, respectively.
Search the File Exchange for galois. There are a handfull of relevant submissions.
Post a new question with a specific title, one that will catch the eye of someone who knows something about encoding, decoding and Galois fields. Carefully select a handfull of tags.
If you have the Parallel Computing Toolbox, a suitable graphical card and some experience, then assess the potential of parallel operations.
Google might find a FORTRAN or C library that you can use to make a mex-file.