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Multiply constant-weight codes (MCWCs) have been recently studied to improvethe reliability of certain physically unclonable function response. In thispaper, we give combinatorial constructions for MCWCs which yield several newinfinite families of optimal MCWCs. Furthermore, we demonstrate that theJohnson type upper bounds of MCWCs are asymptotically tight for fixed weightsand distances. Finally, we provide bounds and constructions of two dimensionalMCWCs.

Constructions of Optimal and Near-Optimal Multiply Constant-Weight Codes