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Hamming Weight


The Hamming weight of a word over an alphabet with a distinguished zero symbol is the number of its nonzero coordinates. For a binary word, it is the number of ones. Equivalently, it is the Hamming distance from the all-zero word. For example, the binary word 10110 has Hamming weight 3.

A constant-weight code consists of codewords of a common Hamming weight (Dzoba 2026).


See also

Codeword, Constant-Weight Code, Hamming Distance

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References

Dzoba, C. "New Lower Bounds for Binary Constant-Weight Codes from Prescribed-Automorphism Search, and Two Quantum Codes Meeting Their Upper Bounds." 16 Oct 2026. https://arxiv.org/abs/2610.24025.

Cite this as:

Weisstein, Eric W. "Hamming Weight." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HammingWeight.html

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