Error Detection and Correction, continued

To detect: δ errors, a distance of δ + 1 is required.

e.g. to detect 1 bit in error requires that there is no word with a distance of 1 from a valid word.

To correct: δ errors, a distance of 2 δ + 1 is required so that even with δ errors, the damaged codeword is the closest to one valid codeword.

Some examples :

Consider a simple encoding of ASCII characters, where we use a parity code [see Tanenbaum 5/e]
We have 7 data bits and a single parity-code bit. Now, what happens if any single bit is corrupted?

• What is the distance of the parity-code?
• What type of errors can it detect?
• What type of errors can it correct?

Consider a code whose only valid code words are :

    0000000000  1111100000  0000011111  1111111111

• What is the distance of this code?
• What type of errors can it detect?
• What type of errors can it correct?