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

This is a graduate-level book aimed at experienced researchers as well as beginning graduate students in finite geometry, incidence geometry, design theory, coding theory and combinatorics. The 21 articles arise from the Fourth Isle of Thorns Conference on Finite Geometries, held in July 2000. The book contains new high-level results at the forefront of the field as well as authoritative surveys. The articles are written so that beginning graduate students can appreciate them. Among the surveys by the invited speakers are P.J. Cameron `Fixed Points and cycles', C.E. Praeger `Implications of line-transitivity for designs', B. Schmidt, `Exponent bounds', which explains recent results on difference sets, and several papers with H. Van Maideghem as co-author on generalized polygons. The editors also contribute: A. Blokhuis, D. Jungnickel, and B. Schmidt `On a class of symmetric divisible designs which are almost projective planes', and D. Luyckx and J.A. Thas discuss the geometry of the quadric in six dimensions. There is also a lengthy and complete survey by J.W.P. Hirschfeld and L. Storme `The packing problem in statistics, coding theory and finite projective spaces: update 2001'. Audience: Researchers as well as beginning graduate students in the areas of finite geometry, incidence geometry, design theory, coding theory and combinatorics will appreciate the surveys and original papers by leaders in these fields.

Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference

A remark on the theorem of Yanushka and Ronan characterizing the “generalized hexagon” H(q) arising from the group G2(q)

In a generalized quadrangle of order (s, s+2), s ≠ 1, regular points cannot occur. Therefore we introduce the notion of R-regularity for points and lines in those generalized quadrangles of order (S, S+2) which contain a spread R. Using these new concepts we give three characterization theorems for P(W(s), (∞)).

R-Regularity and Characterizations of the Generalized Quadrangle P(W(S),(∞))

We will discuss a way to construct new m-systems from known ones by replacing a number of elements of the m-system by a set of other subspaces covering the same points. Further, we investigate in which cases this method can be applied and we find new classes of 1-systems. In the last section, the semipartial geometries arising from 1-systems of W5(q) are studied and it is shown that some of the new 1-systems we have found yield new semipartial geometries.

Joseph A. Thas

Papers

Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference

A remark on the theorem of Yanushka and Ronan characterizing the “generalized hexagon” H(q) arising from the group G2(q)

R-Regularity and Characterizations of the Generalized Quadrangle P(W(S),(∞))

Derivation of m -systems

Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 3