BCH codes as subcodes of Hamming codes
Oliver Pretzel · 1992
Abstract How do you modify a Hamming code to correct two errors? In other words, how can you increase its minimum distance from 3 to 5? You will either have to lengthen the code words or eliminate some of them from your code. Correcting two errors in a long word may not be much better than correcting one error in a short one. So we adopt the second approach. That is, we shall try to produce a double error-correcting subcode of the Hamming code by removing some code words to make the new code sparser.