  The Hamming oracle returns the Hamming distance between an unknown binary
$n$-vector $x$ and a binary query $n$-vector y. The objective is to determine
$x$ uniquely using a sequence of $m$ queries. What are the minimum number of
queries required in the worst case? We consider the query ratio $m/n$ to be our
figure of merit and derive upper bounds on the query ratio by explicitly
constructing $(m,n)$ query matrices. We show that our recursive and algebraic
construction results in query ratios arbitrarily close to zero. Our
construction is based on codes of constant weight. A decoding algorithm for
recovering the unknown binary vector is also described.
