1
$\begingroup$

enter image description here My question is what does [this construction gives a Hamming Distance a distance of 3] means? Why the Hamming Distance of ASCII letter A is 3? How do you determine the Hamming Distance is 3?

This is an excerpt from Computer Network by Andrew S. Tanenbaum page 206.

| cite | improve this question | |
$\endgroup$
  • $\begingroup$ The Hamming code has Hamming distance 3. A particular letter doesn't have Hamming distance, since distance is a two-argument function: it gives the distance (in Hamming metric) between two binary vectors. $\endgroup$ – Yuval Filmus May 21 at 13:07
0
$\begingroup$

A code is a collection of binary vectors of some length $n$, known as codewords. The Hamming distance between two codewords $x,y$ is the number of positions $i$ such that $x_i \neq y_i$. The minimum distance of a code is the minimum Hamming distance between two different codewords.

For example, the Hamming(7,4) code consists of 16 codewords of length 7:

0000000
1110000
1001100
0111100
0101010
1011010
1100110
0010110
1101001
0011001
0100101
1010101
1000011
0110011
0001111
1111111

You can check that any two codewords differ in either 3 or 4 positions. For example, 1010101 and 0100101 differ in the first 3 positions. Therefore the minimum distance of the code is 3.

There is absolutely no meaning for the Hamming distance of a single codeword. Hamming distance is a property of pairs of codewords.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

Tanenbaum is not saying that ASCII character "A" has a particular Hamming distance. Computerphile has a video that may clear things up.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

The Hamming distance between two codes is the number of times there is a different bit between them, for example between 1011 and 1111 a Hamming distance of 1.

The example that you're seeing is code correction. When you send anything through a cable there could be some errors (change of bits 1 to 0 or 0 to 1). So there are some common algorithms that minimise these errors within the domain of Information Theory. In this example they show the binary code of the letter A before and after being received by destination, a Hamming distance of 3 was found means that 3 bits have changed.

I previously implemented some related functions and more details are explained on my GitHub. You can check my git repository if you're interested.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.