Jizhu Nan

New error-correcting pooling designs associated with finite vector spaces

AbstractLet

Lattices Generated by Two Orbits of Subspaces Under Finite Singular Classical Groups

\mathbb{F}_{q}^{n}

Construction of error-tolerance pooling designs in symplectic spaces

be a n-dimensional vector space over

VECTOR INVARIANT IDEALS OF ABELIAN GROUP ALGEBRAS UNDER THE ACTION OF THE SYMPLECTIC GROUPS

\mathbb{F}_{q}

Coinvariants and invariants of the dihedral group in characteristic

. In this paper we construct a new family of inclusion matrices associated with subspaces of

Automorphisms of the zero-divisor graph of 2 × 2 matrix ring over ℤps

\mathbb{F}_{q}^{n}

Invariants of finite groups generated by generalized transvections in the modular case

, and exhibit their disjunct properties.

THE ITERATION DIGRAPHS OF GROUP RINGS OVER FINITE FIELDS

Let be the n + l-dimensional vector space over a finite field 𝔽 q , and let G n+l, n be the singular symplectic group Sp n+l, n (𝔽 q ) where n = 2ν; or the singular unitary group U n+l, n (𝔽 q ) where . For any two orbits M 1 and M 2 of subspaces under G n+l, n , let L 1 (resp., L 2) be the set of all subspaces which are sums (resp., intersections) of subspaces in M 1 (resp., M 2) such that M 2 ⊆ L 1 (resp., M 1 ⊆ L 2). Suppose ℒ is the intersection of L 1 and L 2 containing {0} and . By ordering ℒ by ordinary or reverse inclusion, two families of atomic lattices are obtained. This article characterizes the subspaces in the two lattices and classifies geometricity of these lattices.

Lattices generated by orbits of flats under finite affine-symplectic groups

The paper provides the construction of error-correcting pooling designs with the incidence matrix of two types of subspaces of symplectic spaces over finite fields. As a generalization of Guo et al.’s matrix, we use the general subspaces of type