choosing the galois field for reed-solomon encoding

Question

What determines the size of galois field when using reed-solomon algorithm to encode an arbitrary message of any size? Is it the symbol size, or the size of the message?

For example, if I am to encode ASCII characters, and I use GF(2^8) because ASCII's are 8 bits, I would end up with a maximum codeword length of 2^8 - 1 = 255 ASCII characters. Then I would have to split the message into sub-messages of length 255.

Or, if I use GF(2^s) such that 2^s - 1 >= the length of the message, then there's no need to split the message, but in this case even though I am encoding ASCII characters which are 8 bits, each symbol in the codeword would be considered 2^s bits.

Which is preferred? Or is there any other things that determine the selection of the Galois Field?

Answer 1

The fixed or maximum size of the message determines the symbol size. GF(2^2) for up to 15 nibbles (7.5 bytes), GF(2^8) for up to 255 bytes, GF(2^10) for up to 1023 10 bit symbols or 1278.75 bytes (often used for HDD 512 data byte sectors), GF(2^12) for up to 4095 12 bit symbols or 6142.5 bytes (often used for HDD 4096 data byte sectors).