Partitionable sets, almost partitionable sets, and their applications. Issue 11 (20th July 2020) - Chang, Yanxun; Costa, Simone; Feng, Tao; Wang, Xiaomiao
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.