Question

The following three (10-bit) values are valid codewords. What can you say about the minimal Hamming Distance for the entire code?

00 0110 1000

00 1111 1101

10 0011 1000

Answer 1

Hamming distance:

Hamming distance is the number of differences in the corresponding bits between two binary words or between a set of words of the same size.

Minimum Hamming Distance:

The minimum hamming distance is the smallest Hamming distance between all possible pairs.

The given binary codes are:

Code 1: 0 0 0 1 1 0 1 0 0 0

Code 2: 0 0 1 1 1 1 1 1 0 1

Code 3: 1 0 0 0 1 1 1 0 0 0

Hamming distance between code 1 and code 2 is:

Code 1: 0 0 0 1 1 0 1 0 0 0

Code 2: 0 0 1 1 1 1 1 1 0 1

Hamming distance = 4

Hamming distance between code 1 and code 3 is:

Code 1: 0 0 0 1 1 0 1 0 0 0

Code 3: 1 0 0 0 1 1 1 0 0 0

Hamming distance = 3

Hamming distance between code 2 and code 3 is:

Code 2: 0 0 1 1 1 1 1 1 0 1

Code 3: 1 0 0 0 1 1 1 0 0 0

Hamming distance = 5

Minimum Hamming distance = 3