On the Construction of Multiply Constant-Weight Codes

Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, two methods of constructing MCWCs are presented following the concatenation methodology. In other words, MCWCs are constructed by concatenating approximate outer codes and inner codes. Besides, several classes of optimal MCWCs are derived from these methods. In the first method, the outer codes are [Formula: see text]-ary codes and the inner codes are constant-weight codes over [Formula: see text]. Furthermore, if the outer code achieves the Plotkin bound and the inner code achieves Johnson bound, then the resulting MCWC is optimal. In the second method, the outer codes are [Formula: see text]-ary codes and the inner codes are MCWCs. Furthermore, if the outer code achieves the Plotkin bound and the inner code achieves the Johnson bound, then the resulting MCWC is optimal.