Constructions of 1 1/2-designs from symplectic geometry over finite fields

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• 作者：Zhao Chai ; Rong Quan Feng ; Li Wei Zeng
• 关键词：1 1/2 ; design ; totally isotropic subspace ; generalized symplectic graph ; directed strongly regular graph ; 05B05 ; 05B25 ; 05C25
• 刊名：Acta Mathematica Sinica
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：31
• 期：9
• 页码：1367-1378
• 全文大小：234 KB
• 参考文献：[1]Bose, R. C., Shrikhande, S. S., Singhi, N. M.: Edge regular multigraphs and partial geometric designs. Proc. Internat. Colloq. Combin. Theory, 17, 49鈥?1 (1976)MathSciNet
  [2]Brouwer, A. E., Olmez, O., Song, S. Y.: Directed strongly regular graphs from 1 1/2-designs. European J. Combin., 33(6), 1174鈥?177 (2012)MathSciNet View Article
  [3]Duval, A.: A directed graph version of strongly regular graphs. J. Combin. Theory, Ser. A, 47, 71鈥?00 (1988)MathSciNet View Article
  [4]Klin, M., Munemasa, A., Muzychuk, M., et al.: Directed strongly regular graphs obtained from coherent algebras. Linear Algebra Appl., 377, 83鈥?09 (2004)MathSciNet View Article
  [5]Klin, M., Pech, C., Zieschang, P. H.: Flag algebras of block designs: I. Initial notions, Steiner 2-designs, and generalized quadrangles, MATH-AL-10-1998, Technische Universitat Dresden, preprint, 1998
  [6]Neumaier, A.: t1/2-designs. J. Combin. Theory, Ser. A, 28, 226鈥?48 (1980)MathSciNet View Article
  [7]Olmez, O.: Symmetric 1 1/2-designs and 1 1/2-difference sets. J. Combin. Designs, 22, 252鈥?69 (2014)MathSciNet View Article
  [8]Van Dam, E. R., Spence, E.: Combinatorial designs with two singular values ii. partial geometric designs. Linear Algebra Appli., 396, 303鈥?16 (2005)View Article
  [9]Wan, Z.: Geometry of Classical Groups over Finite Fields, Science Press, Beijing, New York, 2002
  [10]Zeng, L., Chai, Z., Feng, R., et al.: Full automorphism group of the generalized symplectic graph. Sci. China Math., 56(7), 1509鈥?520 (2013)MathSciNet View Article
  
• 作者单位：Zhao Chai (1)
  Rong Quan Feng (1)
  Li Wei Zeng (1)
  
  1. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617

文摘

In this paper, we construct some 1 1/2-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the symplectic space and generalized symplectic graphs. Furthermore, these 1 1/2-designs yield six infinite families of directed strongly regular graphs.