Hamming Distance: What is Max. Distance Between Binary Strings?

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In summary, the Hamming Distance is a measure of the number of positions at which two binary strings of equal length are different. It is calculated by comparing two strings and counting the number of positions where they differ. The maximum possible Hamming Distance between two binary strings is equal to the length of the strings. In coding theory, the Hamming Distance is used to evaluate the error-correcting capabilities of codes. It can also be applied to strings of any type, but is most commonly used with binary strings due to their simpler comparison process.
  • #1
NaturePaper
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Hi,
I don't know where to post this question, so I'm posting it here.

I wish to study some basic properties of Hamming distance (e.g. what is the number of different binary N-bit strings so that the maximum Hamming distance between them is m etc.).

Can anyone refer me some books or papers (/documents etc)?
 
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  • #2
Search your library or the internets for "information theory" and "error correction codes".
 

1. What is meant by "Hamming Distance"?

The Hamming Distance is a measure of the number of positions at which two binary strings of equal length are different. It is used to quantify the similarity between two strings and is named after mathematician Richard Hamming.

2. How is the Hamming Distance calculated?

The Hamming Distance is calculated by comparing two strings and counting the number of positions where they differ. If the two strings are of different lengths, the distance cannot be calculated. The resulting number is the Hamming Distance between the two strings.

3. What is the maximum possible Hamming Distance between two binary strings?

The maximum possible Hamming Distance between two binary strings of equal length is equal to the length of the strings. This means that the two strings are completely different from each other in every position.

4. How is the Hamming Distance used in coding theory?

In coding theory, the Hamming Distance is used to evaluate the error-correcting capabilities of codes. A code with a larger Hamming Distance can detect and correct more errors in a transmitted message than a code with a smaller Hamming Distance.

5. Can the Hamming Distance be used with strings other than binary?

Yes, the concept of the Hamming Distance can be applied to strings of any type, not just binary. However, it is most commonly used with binary strings as they have a simpler comparison process. The Hamming Distance can also be extended to compare strings of different lengths, but the calculation becomes more complex.

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