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New Bounds and Constructions for Multiply Constant-Weight Codes

机译：等重码的新界限和构造

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Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, the bounds of MCWCs and the constructions of optimal MCWCs are studied. First, we derive three different types of upper bounds which improve the Johnson-type bounds given by Chee et al. for some parameters. The asymptotic lower bound of MCWCs is also examined. Then, we obtain the asymptotic existence of two classes of optimal MCWCs, which shows that the Johnson-type bounds for MCWCs with distances 2 Σi=1m wi - 2 or 2mw - 2w are asymptotically exact. Finally, we construct a class of optimal MCWCs with total weight four and distance six by establishing the connection between such MCWCs and a new kind of combinatorial structures. As a consequence, the maximum sizes of MCWCs with total weight less than or equal to four are determined almost completely.
机译：最近引入了乘以恒定权重代码（MCWC），以提高某些物理上不可克隆的功能响应的可靠性。本文研究了MCWC的边界和最优MCWC的构造。首先，我们推导了三种不同类型的上限，它们改进了Chee等人给出的Johnson型界限。对于某些参数。还检查了MCWC的渐近下界。然后，我们获得了两类最优MCWC的渐近存在性，这表明距离为2Σi= 1m wi-2或2mw-2w的MCWC的Johnson型界是渐近精确的。最后，通过建立此类MCWC与新型组合结构之间的联系，构造了一类总重量为4，距离为6的最优MCWC。结果，总重量小于或等于4的MCWC的最大尺寸几乎可以完全确定。

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