Partitionable sets, almost partitionable sets, and their applications. Issue 11 (20th July 2020)

• Record Type: Journal Article
• Authors: Chang, Yanxun; Costa, Simone; Feng, Tao; Wang, Xiaomiao
• Is Part Of: Journal of combinatorial designs. Volume 28:Issue 11(2020:Nov.)
• Page Start: 783
• Page End: 813
• Publication Date: 2020-07-20
• Subjects: almost partitionable set -- balanced sampling plans excluding contiguous unit -- partitionable set -- optical orthogonal code -- whist tournament; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21744
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: This paper introduces almost partitionable sets (APSs) to generalize the known concept of partitionable sets. These notions provide a unified frame to construct Z ‐cyclic patterned starter whist tournaments and cyclic balanced sampling plans excluding contiguous units. The existences of partitionable sets and APSs are investigated. As an application, a large number of optical orthogonal codes achieving the Johnson bound or the Johnson bound minus one are constructed.