Distance-Regular Graphs

Finite Generalized Quadrangles

Determine the value of the variable in each equation.

Basic Algebra = 代数学入門

On etudie les relations entre les codes [n,k] lineaires a deux poids, les ensembles (n,k,h 1 h 2 ) projectifs et certains graphes fortement reguliers

/pdf/the-geometry-of-two-weight-codes-nnndeshbae.pdf

The Geometry of Two-Weight Codes

https://jupiter.math.nctu.edu.tw/~weng/references/distance-regular graphs/cospec_2003.pdf?origin=publication_detail

Which graphs are determined by their spectrum

Combinatorial characterizations of generalized quadrangles with parameters s = q and t = q 2

The variety of (n + 1)× (n + 1) rank one Hermitian matrices over a finite field Fq , which is naturally in one-to-one correspondence with the points of a projective space PG(n, q2) and which gives rise to a cap in the projective space PG(n2+2n, q) on which the group PGL(n+1, q2) acts 2-transitively is studied. Our main result is a geometric characterization of this cap and some of its projections along the lines of the characterization of quadric Veroneseans by Mazzocca and Melone.

http://cage.ugent.be/~hvm/artikels/133.pdf

Hermitian Veroneseans over finite fields

Partial geometries and copolar spaces

In this paper, we give characterizations of the classical generalized quadrangles H(3, q 2) and H(4, q 2), embedded in PG(3, q 2) and PG(4, q 2), respectively. The intersection numbers with lines and planes characterize H(3, q 2), and H(4, q 2) is characterized by its intersection numbers with planes and solids. This result is then extended to characterize all Hermitian varieties in dimension at least 4 by their intersection numbers with planes and solids.

/pdf/characterizations-of-hermitian-varieties-by-intersection-47q750nfvo.pdf

Characterizations of Hermitian varieties by intersection numbers

Let J be a set of types of subspaces of a projective space. Then a collineation or a duality is called J-domestic if it maps no flag of type J to an opposite one. In this paper, we characterize symplectic polarities as the only dualities of projective spaces that map no chamber to an opposite one. This implies a complete characterization of all J-domestic dualities of an arbitrary projective space for all type subsets J. We also completely characterize and classify J-domestic collineations of projective spaces for all possible J.

/pdf/domesticity-in-projective-spaces-1igjosghew.pdf

Joseph A. Thas

Papers

Combinatorial characterizations of generalized quadrangles with parameters s = q and t = q 2

Hermitian Veroneseans over finite fields

Partial geometries and copolar spaces

Characterizations of Hermitian varieties by intersection numbers

Domesticity in projective spaces