New Bounds and Constructions for Multiply Constant-Weight Codes

Xin Wang, Hengjia Wei, Chong Shangguan, Gennian Ge

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number7567498
Pages (from-to)6315-6327
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number11
StatePublished - Nov 2016
Externally publishedYes


  • Gilbert-Varshamov bound
  • Johnson bound
  • Multiply constant-weight codes
  • Plotkin bound
  • concatenation
  • graph decompositions
  • linear programming bound
  • skew almost-resolvable squares
  • spherical codes

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