Let Fq be a finite field with q elements, where q is a power of an odd prime,In this paperl the authors consider a projective space PG(2v + δ + l, Fq) with dimension 2v + δ + l, partitioned into an affine space AG(2...Let Fq be a finite field with q elements, where q is a power of an odd prime,In this paperl the authors consider a projective space PG(2v + δ + l, Fq) with dimension 2v + δ + l, partitioned into an affine space AG(2v + δ + l, Fq) of dimension 2v + δ + l and a hyperplane H = PG(2v + δ + l - 1, Fq) of dimension 2v + δ + l - 1 at infinity, where l ≠0.The points of the hyperplane H are next partitioned into four subsets. A pair of points a and b of the affine space is defined to belong to class i if the line ab meets the subsct i of H. Finally, a family of four-class association schemes are constructed, and parameters are also computed.展开更多
By using nondegenerate and degenerate quadrics in projective space over finite fields of characteristic 2, some association schemes were constructed and their parameters were computed by the authors (see Adv. in Math....By using nondegenerate and degenerate quadrics in projective space over finite fields of characteristic 2, some association schemes were constructed and their parameters were computed by the authors (see Adv. in Math., 3(2000), 120-128 and Acta Math. Appl. Sinica, 1(1999), 96-103). In this note, their polynomial properties, eigenmatrices, imprimitivities, association subschemes and related quotient association schemes are studied.展开更多
Let X_n be the set of n×n symmetric matrices over a finite field F_q,where q is a power of an odd prime.For S_1,S_2 ∈ X_n,we define (S_1,S_2)∈ R_0 iff S_1=S_2;(S_1,S_2)∈R_(r,ε)iff S_1-S_2 is congruent to wher...Let X_n be the set of n×n symmetric matrices over a finite field F_q,where q is a power of an odd prime.For S_1,S_2 ∈ X_n,we define (S_1,S_2)∈ R_0 iff S_1=S_2;(S_1,S_2)∈R_(r,ε)iff S_1-S_2 is congruent to where?=1 or z,z being afixed non-square element of F_q.Then X_n=(X_n,{R_0,R_(r,ε)|1≤r≤n,?=1 or z}) is a non-symmetric association scheme of class 2n on X_n.The parameters of X_n have been computed.And we also prove that X_n is commutative.展开更多
Association scheme is a structure on a finite set that has some special relations among elements in the set. These relations are usually hidden in other relations, so how to derive them out is a problem. The paper giv...Association scheme is a structure on a finite set that has some special relations among elements in the set. These relations are usually hidden in other relations, so how to derive them out is a problem. The paper gives a constructing method of mending parameters of the association schemes, and a new family of association schemes is obtained： quasiFmetric association scheme.展开更多
Taking nondegenerate quadrics in projective space over finite fields of ch.=2, we construct some families of two-class and three-class association schemes, and calculate their parameters. Moreover, for the three-class...Taking nondegenerate quadrics in projective space over finite fields of ch.=2, we construct some families of two-class and three-class association schemes, and calculate their parameters. Moreover, for the three-class association scheme, we also compute all its eigenvalues, corresponding multiplicities and the character table, and prove that it is a p-polynomial association scheme.展开更多
We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility c...We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.展开更多
In this paper, some problems on representations of subspace in a finite field are discussed, a result in [3] is generalized, and a new proof about Singer Difference Sets is given. Finally, a class of association schem...In this paper, some problems on representations of subspace in a finite field are discussed, a result in [3] is generalized, and a new proof about Singer Difference Sets is given. Finally, a class of association schemes are constructed by all affine hyperplanes in a finite field and the parameters are computed.展开更多
For fiber-commutative coherent configurations,we show that Krein parameters can be defined essentially uniquely.As a consequence,the general Krein condition reduces to positive semidefiniteness of finitely many matric...For fiber-commutative coherent configurations,we show that Krein parameters can be defined essentially uniquely.As a consequence,the general Krein condition reduces to positive semidefiniteness of finitely many matrices determined by the parameters of a coherent configuration.We mention its implications in the coherent configuration defined by a generalized quadrangle.We also simplify the absolute bound using the matrices of Krein parameters.展开更多
文摘Let Fq be a finite field with q elements, where q is a power of an odd prime,In this paperl the authors consider a projective space PG(2v + δ + l, Fq) with dimension 2v + δ + l, partitioned into an affine space AG(2v + δ + l, Fq) of dimension 2v + δ + l and a hyperplane H = PG(2v + δ + l - 1, Fq) of dimension 2v + δ + l - 1 at infinity, where l ≠0.The points of the hyperplane H are next partitioned into four subsets. A pair of points a and b of the affine space is defined to belong to class i if the line ab meets the subsct i of H. Finally, a family of four-class association schemes are constructed, and parameters are also computed.
基金The NNSF (19571024) of China Hebei Province Education Committee Fund (98103).
文摘By using nondegenerate and degenerate quadrics in projective space over finite fields of characteristic 2, some association schemes were constructed and their parameters were computed by the authors (see Adv. in Math., 3(2000), 120-128 and Acta Math. Appl. Sinica, 1(1999), 96-103). In this note, their polynomial properties, eigenmatrices, imprimitivities, association subschemes and related quotient association schemes are studied.
文摘Let X_n be the set of n×n symmetric matrices over a finite field F_q,where q is a power of an odd prime.For S_1,S_2 ∈ X_n,we define (S_1,S_2)∈ R_0 iff S_1=S_2;(S_1,S_2)∈R_(r,ε)iff S_1-S_2 is congruent to where?=1 or z,z being afixed non-square element of F_q.Then X_n=(X_n,{R_0,R_(r,ε)|1≤r≤n,?=1 or z}) is a non-symmetric association scheme of class 2n on X_n.The parameters of X_n have been computed.And we also prove that X_n is commutative.
文摘Association scheme is a structure on a finite set that has some special relations among elements in the set. These relations are usually hidden in other relations, so how to derive them out is a problem. The paper gives a constructing method of mending parameters of the association schemes, and a new family of association schemes is obtained： quasiFmetric association scheme.
基金This project is supported by the National Natural Science Foundation of China!No.19571024
文摘Taking nondegenerate quadrics in projective space over finite fields of ch.=2, we construct some families of two-class and three-class association schemes, and calculate their parameters. Moreover, for the three-class association scheme, we also compute all its eigenvalues, corresponding multiplicities and the character table, and prove that it is a p-polynomial association scheme.
基金supported by the European Regional Development Fund through the program COMPETEby the Portuguese Government through the FCT—Fundacao para a Ciencia e a Tecnologia under the project PEst—C/MAT/UI0144/2013+1 种基金partially supported by Portuguese Funds trough CIDMA—Center for Research and development in Mathematics and Applications,Department of Mathematics,University of Aveiro,3810-193,Aveiro,Portugalthe Portuguese Foundation for Science and Technology(FCT-Fundacao para a Ciencia e Tecnologia),within Project PEst-OE/MAT/UI4106/2014
文摘We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.
基金the Natural Science Foundation of Hebei Province (No.A2008000135)
文摘In this paper, some problems on representations of subspace in a finite field are discussed, a result in [3] is generalized, and a new proof about Singer Difference Sets is given. Finally, a class of association schemes are constructed by all affine hyperplanes in a finite field and the parameters are computed.
文摘For fiber-commutative coherent configurations,we show that Krein parameters can be defined essentially uniquely.As a consequence,the general Krein condition reduces to positive semidefiniteness of finitely many matrices determined by the parameters of a coherent configuration.We mention its implications in the coherent configuration defined by a generalized quadrangle.We also simplify the absolute bound using the matrices of Krein parameters.
