919 research outputs found
Small blocking sets of hermitian designs
AbstractA Hermitian design H(q) consists of the points and Hermitian unitals of PG(2,q2). A committee of H(q) is a blocking set of H(q) of minimum cardinality b(H(q)). It is proved that the committees of H(3) are the lines of PG(2, 9) and, for all odd q, that 2q + 2 ≤b(H(q)) < (1 + 7 ln q)(q2 + 1)q−1
Intersection sets, three-character multisets and associated codes
In this article we construct new minimal intersection sets in
sporting three intersection numbers with hyperplanes; we
then use these sets to obtain linear error correcting codes with few weights,
whose weight enumerator we also determine. Furthermore, we provide a new family
of three-character multisets in with even and we
also compute their weight distribution.Comment: 17 Pages; revised and corrected result
The use of blocking sets in Galois geometries and in related research areas
Blocking sets play a central role in Galois geometries. Besides their intrinsic geometrical importance, the importance of blocking sets also arises from the use of blocking sets for the solution of many other geometrical problems, and problems in related research areas. This article focusses on these applications to motivate researchers to investigate blocking sets, and to motivate researchers to investigate the problems that can be solved by using blocking sets. By showing the many applications on blocking sets, we also wish to prove that researchers who improve results on blocking sets in fact open the door to improvements on the solution of many other problems
Blocking sets of the Hermitian unital
It is known that the classical unital arising from the Hermitian curve in PG(2,9) does not have a 2-coloring without monochromatic lines. Here we show that for q≥4 the Hermitian curve in PG(2,q2) does possess 2-colorings without monochromatic lines. We present general constructions and also prove a lower bound on the size of blocking sets in the classical unital
On the dual code of points and generators on the Hermitian variety H(2n+1,q²)
We study the dual linear code of points and generators on a non-singular Hermitian variety H(2n + 1, q(2)). We improve the earlier results for n = 2, we solve the minimum distance problem for general n, we classify the n smallest types of code words and we characterize the small weight code words as being a linear combination of these n types
- …