What is Minimum Hamming Distance? Give example
The minimum Hamming distance is the smallest hamming distance between all possible pairs in a set of words. For example, if the codeword 00000 is sent and 01101 is received, 3 bits are in error and the Hamming distance between the two is d(00000, 01101) =3.
In particular, a code C is said to be k error detecting if, and only if, the minimum Hamming distance between any two of its codewords is at least k+1. For example, consider the code consisting of two codewords "000" and "111". The hamming distance between these two words is 3, and therefore it is k=2 error detecting.
The Hamming Code is simply the use of extra parity bits to allow the identification of an error. Write the bit positions starting from 1 in binary form (1, 10, 11, 100, etc). All the bit positions that are a power of 2 are marked as parity bits (1, 2, 4, 8, etc). All the other bit positions are marked as data bits
The minimum Hamming distance is used to define some essential notions in coding theory, such as error detecting and error correcting codes. ... In other words, a code is k-errors correcting if, and only if, the minimum Hamming distance between any two of its codewords is at least 2k+1.
Example : Find the distance between the vectors 01101010 and 11011011. They differ in four places, so the Hamming distance d(01101010,11011011) = 4.
Example : Find the distance between the vectors 01101010 and 11011011. They differ in four places, so the Hamming distance d(01101010,11011011) = 4.
Hamming distance is a metric for comparing two binary data strings. While comparing two binary strings of equal length, Hamming distance is the number of bit positions in which the two bits are different.
The Hamming distance between two strings, a and b is denoted as d(a, b).
It is used for error detection or error correction when data is transmitted over computer networks. It is also using in coding theory for comparing equal length data words.
Thus the Hamming distance between two vectors is the number of bits we must change to change one into the other. Example Find the distance between the vectors 01101010 and 11011011. They differ in four places, so the Hamming distance
d(01101010,11011011)
= 4.
The Hamming distance between two strings, a and b is denoted as d(a, b).
It is used for error detection or error correction when data is transmitted over computer networks. It is also using in coding theory for comparing equal length data words.
Thus the Hamming distance between two vectors is the number of bits we must change to change one into the other. Example Find the distance between the vectors 01101010 and 11011011. They differ in four places, so the Hamming distance
d(01101010,11011011)
= 4.
Thus the Hamming distance between two vectors is the number of bits we must change to change one into the other. Example Find the distance between the vectors 01101010 and 11011011. They differ in four places, so the Hamming distance d(01101010,11011011) = 4.