Due March 24
1. Correct each of the following Hamming strings:
1 1 0 0 0 1 1
0 0 0 1 1 0 0
1 1 1 0 0 0 0 0 0 0 0 0 0 0 1
2. Find the upper bound (by sphere-packing) of the number of messages that
would be in a codebook for a 12-bit code for
- single error-correction
- double error-correction
- triple error correction
3. For the code book below interpret the message 0 0 0 0 0 1 1 0, for
the case of double error correction, and single error correction with
triple error detection.
1 1 1 1 1 0 1 1
0 0 0 0 0 0 1 1
1 1 0 0 0 1 0 0
4. Consider the 8 bit Hamming Code for single error detection with
double error detection. Of the 256 8-bit sequences, how many
- are valid code words?
- are correctable (one error)?
- have 2 errors?