| Some Results on Minimum Aberration Mixed-level （2^r）2^n Factorial Designs |
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| 引用本文： | SHI Cheng-tang~1 ZHANG Dan~2 CHEN Bao-ting~3 LI Yu-kai~1 (1.Department of Trade and Economics,Zhengzhou Electric Power College,Zhengzhou 450004,China, 2.Department of Basic Course,Henan Vocational College of Economy and Trade,Zhengzhou 450053,China, 3.Henan Province Computer Center,Zhengzhou 450008,China). Some Results on Minimum Aberration Mixed-level （2^r）2^n Factorial Designs[J]. 数学季刊, 2007, 22(1): 79-86 |
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| 作者姓名： | SHI Cheng-tang~1 ZHANG Dan~2 CHEN Bao-ting~3 LI Yu-kai~1 (1.Department of Trade and Economics Zhengzhou Electric Power College Zhengzhou 450004 China 2.Department of Basic Course Henan Vocational College of Economy and Trade Zhengzhou 450053 China 3.Henan Province Computer Center Zhengzhou 450008 China) |
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| 作者单位： | 1.Department of Trade and Economics，Zhengzhou Electric Power College，Zhengzhou 450004，China; 2.Department of Basic Course，Henan Vocational College of Economy and Trade，Zhengzhou 450053，China; 3.Henan Province Computer Center，Zhengzhou 450008，China |
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| 基金项目： | Supported by NNSF of China(10231030) |
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| 摘 要： | Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4.In this paper,by introducing a concept of consulting design and based on the connection between factorial design theory and cod- ing theory,we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level (2~r)2~n factorial design to that of its consulting design.Consequently,a general rule for identifying minimum aberration (2~r)2~n factorial designs through their con- sulting designs is established.It is an improvement and generalization of the related result in Mukerjee and Wu(2001).
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| 关 键 词： | 最小象差 混合水平 因子设计 编码理论 |
Some Results on Minimum Aberration Mixed-level (2~r)2~n Factorial Designs |
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| SHI Cheng-tang ZHANG Dan CHEN Bao-ting LI Yu-kai. Some Results on Minimum Aberration Mixed-level (2~r)2~n Factorial Designs[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(1): 79-86 |
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| Authors: | SHI Cheng-tang ZHANG Dan CHEN Bao-ting LI Yu-kai |
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| Affiliation: | [1]Department of Trade and Economics, Zhengzhou Electric Power College, Zhengzhou 450004, China [2]Department of Basic Course, Henan Vocational College of Economy and Trade, Zhengzhou 450053, China [3]Henan Province Computer Center, Zhengzhou 450008, China |
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| Abstract: | Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4.In this paper,by introducing a concept of consulting design and based on the connection between factorial design theory and cod- ing theory,we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level (2~r)2~n factorial design to that of its consulting design.Consequently,a general rule for identifying minimum aberration (2~r)2~n factorial designs through their con- sulting designs is established.It is an improvement and generalization of the related result in Mukerjee and Wu(2001). |
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| Keywords: | coding theory consulting design minimum aberration mixed-level regular wordlength pattern |
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