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The Exact Multiplicative Complexity of the Hamming Weight Function
Published
Author(s)
Rene C. Peralta, Joan Boyar
Abstract
We consider the problem of computing the Hamming weight of an n-bit vector using a circuit with gates for addition and multiplication modulo 2 (alternatively, XOR and conjunction gates) only. The number of multiplications necessary and sufficient to build such a circuit is called the multiplicative complexity of the Hamming weight function. We prove the exact multiplicative complexity of the Hamming weight function on n variables is n minus the Hamming weight of the binary representation of n.
Peralta, R.
and Boyar, J.
(2005),
The Exact Multiplicative Complexity of the Hamming Weight Function, Proceedings published by Springer-Verlag
(Accessed October 7, 2025)