Minimum weight
Encyclopedia
In error-correcting coding, the minimum Hamming weight
, commonly referred to as the minimum weight wmin of a code is the weight of the lowest-weight code word. The weight w of a code word is the number of 1s in the word. For example the word 11001010 has a weight of 4.
In a linear block code the minimum weight is also the minimum Hamming distance (dmin) and defines the error correction capability of the code. If wmin = n, then dmin = n and the code will correct up to dmin/2 errors.
Hamming weight
The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a string of bits, this is the number of 1's in the string...
, commonly referred to as the minimum weight wmin of a code is the weight of the lowest-weight code word. The weight w of a code word is the number of 1s in the word. For example the word 11001010 has a weight of 4.
In a linear block code the minimum weight is also the minimum Hamming distance (dmin) and defines the error correction capability of the code. If wmin = n, then dmin = n and the code will correct up to dmin/2 errors.