  We introduce the class of multiply constant-weight codes to improve the
reliability of certain physically unclonable function (PUF) response. We extend
classical coding methods to construct multiply constant-weight codes from known
$q$-ary and constant-weight codes. Analogues of Johnson bounds are derived and
are shown to be asymptotically tight to a constant factor under certain
conditions. We also examine the rates of the multiply constant-weight codes and
interestingly, demonstrate that these rates are the same as those of
constant-weight codes of suitable parameters. Asymptotic analysis of our code
constructions is provided.
