Answer 6—Given a specific number (N) of check bits, there are 2^N equivalent Hamming codes that can be constructed by arbitrarily choosing each check bit to have either even or odd parity within its group of data bits. As long as the encoder and the decoder use the same definitions for the check bits, all of the properties of the Hamming code are preserved. Sometimes it’s useful to define the check bits so that an encoded word of all zeros or all ones is always detected as an error.

Contributor: David Tweed