#### Question 7.9 Question 7.10

### Hamming distance

The number of bits difference between pairs of coded blocks (code words) is a very important property of the code, and is known as the Hamming distance. The greater the Hamming distance, the more dissimilar the code words or blocks and the better the chance of detecting or correcting errors.

#### A block code with a Hamming distance of p can detect up to p – 1 errors, and correct (p – 1) / 2 errors.

Shown here is a subset of code words from a (4,7) code which can be seen to have a Hamming distance of 3 between each code word. If this were the minimum distance between all code words in the set then this code would be classed as having a minimum Hamming distance dmin = 3. The code could thus detect up to two errors and correct one error. |