hamming_distance.md

aliases	author	created	modified	tags	title
Hamming Distance Minimum Hamming Distance MHD	Maneesh Sutar	2024-06-01	2025-04-14		Hamming Distance

Hamming Distance

==The number of bit positions where two codes differ==

e.g.
1010 and 1100 : 3
1010 and 1011: 1
1010 and 1111 : 2

Minimum Hamming Distance

In a ==given system of valid code words==, it is the ==minimum number of bit positions where any two VALID code words differ==

e.g.
Suppose in a system of data transmission, ==for error detection, each bit is repeated thrice==.
Thus, a data (code word) is valid, only if each of its bits are repeated thrice

Original data: 010
Sent data: 000111000
Original data: 011
Sent data: 000111111

By flipping 1 bit in original data, 3 bits are flipped in the valid code word
Try adding more bits to original data, minimum 3 times more bits will be added to a valid data.

Thus the minimum hamming distance is 3.

Number of bit-errors which are detectable = MHD - 1
Number of bit-error which are correctable = floor ( (MHD - 1) / 2 )