Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776928 | Discrete Mathematics | 2017 | 11 Pages |
Abstract
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,wv) with block size k, which is denoted by w-cyclic k-HGDD of type (u,wv). The necessary conditions of such a design, namely u,vâ¥k, (uâ1)(vâ1)wâ¡0(modkâ1) and u(uâ1)v(vâ1)wâ¡0(modk(kâ1)), are shown to be sufficient for k=3. As an application, we give a complete solution of the existence problem of perfect three-dimensional optical orthogonal codes of weight three with both at most one-pulse per spatial plane and at most one-pulse per wavelength plane properties.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Suhui Dai, Yanxun Chang, Lidong Wang,