Minimum weight

In error-correcting coding, the minimum Hamming weight, commonly referred to as the minimum weight w_min of a code is the weight of the lowest-weight non-zero 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 (d_min) and defines the error correction capability of the code. If w_min = n, then d_min = n and the code will correct up to d_min/2 errors.