Constructions of Strictly m‐Cyclic and Semi‐Cyclic H(m, n, 4, 3). Issue 6 (16th February 2015)

• Record Type: Journal Article
• Authors: Bao, Jingjun; Ji, Lijun
• Is Part Of: Journal of combinatorial designs. Volume 24:Issue 6(2016:Jun.)
• Page Start: 249
• Page End: 264
• Publication Date: 2015-02-16
• Subjects: 3‐design -- strictly cyclic -- optical orthogonal code -- H design; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21424
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: An H ( m, n, 4, 3 ) is a triple ( X, T, B ), where X is a set of m n points, T is a partition of X into m disjoint sets of size n and B is a set of 4‐element transverses of T, such that each 3‐element transverse of T is contained in exactly one of them. If the full automorphism group of an H ( m, n, 4, 3 ) admits an automorphism α consisting of n cycles of length m (resp. m cycles of length n ), then this H ( m, n, 4, 3 ) is called m ‐cyclic (resp. semi‐cyclic). Further, if all block‐orbits of an m ‐cyclic (resp. semi‐cyclic) H ( m, n, 4, 3 ) are full, then it is called strictly cyclic. In this paper, we construct some infinite classes of strictly m ‐cyclic and semi‐cyclic H ( m, n, 4, 3 ), and use them to give new infinite classes of perfect two‐dimensional optical orthogonal codes with maximum collision parameter λ = 2 and AM‐OPPTS/AM‐OPPW property.