Quaderni Elettronici del Seminario di Geometria Combinatoria
16E (Febbraio 2005), 1--39Università degli Studi di Roma "La Sapienza" - Dipartimento di Matematica |

Dieter JUNGNICKEL

(Febbraio 2005)

In particular, we will discuss what is usually called the
*classical* parameter series. Here the nicest examples are
closely related to perfect codes and to some classical relative
difference sets associated with affine geometries;
moreover, the matrices in question can be characterized as the unique
(up to equivalence) BGW-matrices for the given
parameters with minimum *q*-rank. One can also obtain a wealth of
monomially inequivalent examples and determine
the *q*-ranks of all these matrices by exploiting a connection with
linear shift register sequences.

There are also many applications of BGW-matrices to constructions of designs and graphs; we will restrict ourselves to just one construction method for symmetric designs due to Yury Ionin, for which we will work out an example in detail.

Author:

- Dieter Jungnickel
- Lehrstuhl fuer Diskrete Mathematik,

Optimierung und Operations Research

Universitaet Augsburg

D-86153 Augsburg, Germany

e-mail: jungnickel@math.uni-augsburg.de

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