New bounds and constructions for multiply constant-weight codes

• DOI: 10.48550/arxiv.1512.08220
• Publication Date: 2015-01-01
• Authors: Xin Wang; Hengjia Wei; Chong Shangguan; Gennian Ge
• Keywords: Constant (computer programming); Asymptotically optimal algorithm; Weight function; Minimum weight

Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, bounds MCWCs and constructions optimal are studied. Firstly, we derive three different types upper which Johnson-type given by Chee {\sl et al.} in some parameters. The asymptotic lower bound is also examined. Then obtain existence two classes MCWCs, shows that for with distances $2\sum_{i=1}^mw_i-2$ or $2mw-w$ asymptotically exact. Finally, construct a class total weight four distance six establishing connection between such new kind combinatorial structures. As consequence, maximum sizes less than equal determined almost completely.