The linked wiki article said that given 12 bits, the BG code can encode them as 24 bits with the ability to correct up to 3 bit errors and detect up to 7. If I'm understanding RS codes correctly, an RS code with 12 data and 12 parity bits would be able to correct up to 6 bit errors and detect up to 12. So what is the advantage of a BG code in that case?
> By adding t check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to and including t erroneous symbols, OR locate and correct up to and including ⌊t/2⌋ erroneous symbols at unknown locations
So it looks like you would have to choose between, either:
A) correcting 6 bits OR
B) detecting 12 bit errors.
[1] https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_cor...
if the number of corrupted bits is no more than six, you can reconstruct the original message
if the number of corrupted bits is between 6 and 12, you will detect the corruption
if the number of corrupted bits is larger than 12, you may or may not detect the corruption.