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Motivated by the application to three-dimensional optical orthogonal codes, we consider the constructions for a w -cyclic holey group divisible design of type ( u , w v ) with block size k , which is denoted by w -cyclic k -HGDD of type ( u , w v ) . The necessary conditions of such a design, namely u , v ≥ k , ( u − 1 ) ( v − 1 ) w ≡ 0 ( m o d k − 1 ) and u (...
Suppose Kv is the complete undirected graph with v vertices and G is a finite simple undirected graph without isolated vertices. A G-packing of Kv is a pair (X,B), where X is the vertex set of Kv and B is a collection of edge-disjoint subgraphs (blocks) isomorphic to G in Kv. A G-packing (X,B) is called resolvable if B can be partitioned into parallel classes such that every vertex is contained in...
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