I am using a Reed-Solomon FEC implementation in GF(1024) to correct T=15 errors in a given codeword.
In the particular implementation though, I know for a fact that for each transmitted symbols, the corresponding received (potentially error'ed) symbol will always be one of a given set of symbols. The set depends on the value of the original symbol, and can contain anywhere from 32 to 243 members.
So for example if my original symbol is A0='0000000000', then the received symbol will always belong to a known set S(A0) which obviously contains A0 and some other symbols, never to exceed 243 symbols total per set. If A!=B then S(A)!=S(B) (but the intersection of S(A) and S(B) in general is non-empty).
Can you think of some optimization that I can use in order to reduce the parity of the code, given that I know that there is a limited number of possible received symbols for each transmitted symbol?