The Hamming weight of the non-adjacent form is studied in relation to the Hamming weight of the standard binary expansion. In particular, we investigate the expected Hamming weight of the NAF of an n-digit binary expansion with k ones where k is either fixed or proportional to n. The expected Hamming weight of NAFs of binary expansions with large (≥ n/2) Hamming weight is studied. Finally, the covariance of the Hamming weights of the binary expansion and the NAF is computed. Asymptotically, these Hamming weights become independent and normally distributed.
Key words and phrases
Non-adjacent form binary expansion Hamming weight transducer generating function Omega operator singularity analysis quasi-power theorem multivariate asymptotics
Mathematics subject classification number
11A63 68W40 68Q45 05A16 05A15
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