On the number of optimal base 2 representations of integers
We study representations of integers n in binary expansions using the digits 0, +/- 1. We analyze the average number of such representations of minimal "weight" (= number of non-zero digits). The asymptotic main term of this average involves a periodically oscillating function, which is analyzed in some detail. The main tool is the construction of a measure on [-1,1], which encodes the number of representations.
signed digit expansions minimal hamming weight elliptic curve cryptography