Association schemes based on partial subspaces of type (2, 0, 1) in singular symplectic space

Zengti LI; Guanghui FENG

doi:10.3868/s140-DDD-026-0001-x

Front. Math. China ›› 2026, Vol. 21 ›› Issue (1) :1 -13. DOI: 10.3868/s140-DDD-026-0001-x

RESEARCH　ARTICLE

Association schemes based on partial subspaces of type (2, 0, 1) in singular symplectic space

Zengti LI ¹
, Guanghui FENG ²

Author information +

History +

PDF (395KB)

Abstract

Let $F q (2 ν + l)$ be the $(2 ν + l)$ -dimensional singular symplectic space over the finite field $F q$ , $K$ be a fixed maximal totally isotropic subspace in $F q (2 ν + l)$ , and $Ω$ be the set of all subspaces of type $(1, 0, 0)$ not contained in $K$ . In this paper, we construct a class of association schemes by using all subspaces of type $(2, 0, 1)$ that contain a subspace from $Ω$ , and compute all intersection numbers of the constructed schemes.

Keywords

Association schemes / singular symplectic space / finite field

Cite this article

Download citation ▾

Zengti LI, Guanghui FENG. Association schemes based on partial subspaces of type (2, 0, 1) in singular symplectic space. Front. Math. China, 2026, 21(1): 1-13 DOI:10.3868/s140-DDD-026-0001-x

登录浏览全文

4963

注册一个新账户忘记密码

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Bannai E. , Ito, T., Algebraic Combinatorics I: Association Schemes, Menlo Park, CA: Benjamin/Cummings, 1984

[2]	Brouwer A.E., Cohen, A.M. , Neumaier, A., Distance-Regular Graphs, Berlin: Springer-Verlag, 1989

[3]	Brouwer A.E.. and Haemers, W.H., Association schemes, Chapter 15, In: Handbook of Combinatorics (Graham, R., Grötschel, M. and Lovász, L. eds.), Amsterdam: Elsevier Science, 1995

[4]	Faradžev I.A. Ivanov A.A. Klin M.H. Woldar A.J. , Investigations in Algebraic Theory of Combinatorial Objects, Dordrecht: Kluwer Academic Publishers, 1994

[5]	Gao Y. , He, Y.F. . Association schemes based on the subspaces of type (m, s, 0) in singular symplectic space over finite fields. Linear Algebra Appl. 2013; 439(11): 3435–3444

[6]	Godsil C.D., Algebraic Combinatorics, New York: Chapman & Hall, 1993

[7]	Guo J., Wang, K.S. , Li, F.G. . Association schemes based on maximal isotropic subspaces in singular classical spaces. Linear Algebra Appl. 2009; 430(2/3): 747–755

[8]	Guo J., Wang, K.S. , Li, F.G. . Association schemes based on maximal totally isotropic subspaces in singular pseudo-symplectic spaces. Linear Algebra Appl. 2009; 431(10): 1898–1909

[9]	Rieck M.Q. . Association schemes based on isotropic subspaces, part I. Discrete Math. 2005; 298(1): 301–320

[10]	Wan Z.X., Geometry of Classical Groups Over Finite Fields, 2nd Edition, Beijing: Science Press, 2002

[11]	Wan Z.X.Dai Z.D.Feng C.Y.Yang B.J., Some Research on Finite Geometry and Incomplete Block Designs, Beijing: Science Press, 1966

[12]	Wang K.S., Guo, J. , Li, F.G. . Suborbits of subspaces of type (m, k) under finite singular general singular groups. Linear Algebra Appl. 2009; 431(8): 1360–1366

[13]	Wang K.S., Guo, J. , Li, F.G. . Association schemes based on attenuated spaces. European J. Combin. 2010; 31(1): 297–305

[14]	Wang K.S., Li, F.G., Guo, J. , Ma, J. . Association schemes coming from minimal flats in classical polar spaces. Linear Algebra Appl. 2011; 435(1): 163–174

[15]	Wei H.Z. , Wang, Y.X. . Suborbits of the finite pseudo-symplectic group of characteristic two on the transitive set of m-dimensional totally isotropic subspaces. Acta Math. Sin., Chin. Ser. 1995; 38(5): 696707

[16]	Wei H.Z. , Wang, Y.X. . Suborbits of the transitive set of subspaces of type (m, 0) under finite classical groups. Algebra Colloq. 1996; 3(1): 73–84