Ae Andries Brouwer

A new table of constant weight codes

A table of binary constant weight codes of length nl28 is presented. Explicit constructions are given for most of the 600 codes in the table; the majority of these codes are new. The known techniques for constructing constant weight codes are surveyed, and a table of (unrestricted) binary codes of length nl28 is given

An updated table of minimum-distance bounds for binary linear codes

In 1973 Helgert and Sfinaff published a table of upper and lower bounds on the maximum minimum-distance for binary linear error-correcting codes up to length 127 . This article presents an updated table incorporating numerous improvements that have appeared since then. To simplify the updating task the author has developed a computer program that systematically investigates the consequences of each improvement by applying several well-known general code-construction techniques. This program also made it possible to check the original table. Furthermore, it offers a quick and reliable update service for future improvements.

Group divisible designs with block-size four

It is proved that the obvious necessary conditions for the existence of a group divisible design with k=4 are sufficient, except for the cases corresponding to the non-existing transversal designs T[4,1;2] and T[4,1;6].

Optimal packings of K4's into a Kn

In this paper we determine the maximum cardinality of a packing of K4s into Kn, that is, construct optimal constant weight codes with weight 4 and minimum distance 6.

THE STRUCTURE OF NEAR POLYGONS WITH QUADS

We develop a structure theory for near polygons with quads. Main results are the existence of sub 2j-gons for 2⩽j⩽d and the nonexistence of regular sporadic 2d-gons for d⩾4 with s>1 and t2>1 and t3≠t2(t2+1).

Bounds for binary codes of length less than 25

Improved bounds for A(n,d) , the maximum number of codewords in a (linear or nonlinear) binary code of word length n and minimum distance d , and for A(n,d,w) , the maximum number of binary vectors of length n , distance d , and constant weight w in the range n \leq 24 and d \leq 10 are presented. Some of the new values are A

Near polygons and Fischer spaces

In this paper we exploit the relations between near polygons with lines of size 3 and Fischer spaces to classify near hexagons with quads and with lines of size three. We also construct some infinite families of near polygons.

The blocking number of an affine space

Abstract It is proved that the minimum cardinality of a subset of AG(k, q) which intersects all hyperplanes is k(q − 1) + 1. In case k = 2 this settles a conjecture of J. Doyen.

On the p -Rank of the Adjacency Matrices of Strongly Regular Graphs

AbstractLet Γ be a strongly regular graph with adjacency matrix A. Let I be the identity matrix, and J the all-1 matrix. Let p be a prime. Our aim is to study the p-rank (that is, the rank over