Semi–cyclic Holey Group Divisible Designs and Applications to Sampling Designs and Optical Orthogonal Codes |
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| Authors: | Tao Feng Xiaomiao Wang Ruizhong Wei |
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| Affiliation: | 1. Institute of Mathematics, Beijing Jiaotong University, Beijing, P. R. China;2. Department of Mathematics, Ningbo University, Ningbo, P. R. China;3. Department of Computer Science, Lakehead University, Thunder Bay, ON, Canada |
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| Abstract: | We consider the existence problem for a semi‐cyclic holey group divisible design of type  with block size 3, which is denoted by a 3‐SCHGDD of type  . When t is odd and  or t is doubly even and  , the existence problem is completely solved; when t is singly even, many infinite families are obtained. Applications of our results to two‐dimensional balanced sampling plans and optimal two‐dimensional optical orthogonal codes are also discussed. |
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| Keywords: | holey group divisible design semi‐cyclic two‐dimensional balanced sampling plan two‐dimensional optical orthogonal code |
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