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