In some error-correcting codes, for certain errors, we may be able to correct more errors than Theorem 4.1 suggests: that is, the minimum distance is 2t + 1, but we can correct certain sequences of > t errors. Weve already seen that we cant successfully correct every such sequence of errors, but we can successfully handle some sequences of errors using the standard algorithm for error correction (returning the closest codeword).

4.22 The Repetition3 code with 4-bit messages is only guaranteed to correct 1 error. Whats the largest number of errors that can possibly be corrected successfully by this code? Explain your answer.

4.23 In the Hamming code, we never correct more than 1 error successfully. Prove why not.

4.24 (programming required) Write a program, in a programming language of your choice, to verify that any two codewords in the Hamming code differ in at least three bit positions.