Association schemes have close connections with coding, design and finite group theory, etc. In 1965, Wan Zhe-xian first discussed the association schemes based on the n×n Hermitian matrices over finite fields, a...Association schemes have close connections with coding, design and finite group theory, etc. In 1965, Wan Zhe-xian first discussed the association schemes based on the n×n Hermitian matrices over finite fields, and calculated their parameters when n=2. Later,Wang Yang-xian gave a recurrence calculation formula of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
For the association schemes of quadratic forms over a finite field of characteristic two, the parameters of this association scheme are discussed by using matrix skill. For n=2, 3 , all the parameters are computed. Fo...For the association schemes of quadratic forms over a finite field of characteristic two, the parameters of this association scheme are discussed by using matrix skill. For n=2, 3 , all the parameters are computed. For n≥3 , the formulas of parameters P * 2 -2j+1 and related recursion formulas of the general parameters P * ** are obtained.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
文摘Association schemes have close connections with coding, design and finite group theory, etc. In 1965, Wan Zhe-xian first discussed the association schemes based on the n×n Hermitian matrices over finite fields, and calculated their parameters when n=2. Later,Wang Yang-xian gave a recurrence calculation formula of
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.
文摘For the association schemes of quadratic forms over a finite field of characteristic two, the parameters of this association scheme are discussed by using matrix skill. For n=2, 3 , all the parameters are computed. For n≥3 , the formulas of parameters P * 2 -2j+1 and related recursion formulas of the general parameters P * ** are obtained.
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.
