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 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.^[1]

References

1. ^ Stern & Mahmoud, Communications System Design, Prentice Hall, 2004, p 477ff.

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