Constructions of Strictly m‐Cyclic and Semi‐Cyclic H(m, n, 4, 3). Issue 6 (16th February 2015) - Bao, Jingjun; Ji, Lijun
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.