Sascha Kurz

Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance

In this paper we construct constant dimension codes with prescribed minimum distance. There is an increased interest in subspace codes in general since a paper [13] by Kotter and Kschischang where they gave an application in network coding. There is also a connection to the theory of designs over finite fields. We will modify a method of Braun, Kerber and Laue [7] which they used for the construction of designs over finite fields to construct constant dimension codes. Using this approach we found many new constant dimension codes with a larger number of codewords than previously known codes. We finally give a table of the best constant dimension codes we found.

On the inverse power index problem

Weighted voting games are frequently used in decision making. Each voter has a weight and a proposal is accepted if the weight sum of the supporting voters exceeds a quota. One line of research is the efficient computation of so-called power indices measuring the influence of a voter. We treat the inverse problem: Given an influence vector and a power index, determine a weighted voting game such that the distribution of influence among the voters is as close as possible to the given target value. We present exact algorithms and computational results for the Shapley–Shubik and the (normalized) Banzhaf power index.

Optimal binary subspace codes of length 6, constant dimension 3 and minimum distance 4

It is shown that the maximum size of a binary subspace code of packet length

On the Hegselmann-Krause conjecture in opinion dynamics

v=6

There Are Integral Heptagons, no Three Points on a Line, no Four on a Circle

, minimum subspace distance

Minimal proper non-IRUP instances of the one-dimensional cutting stock problem

d=4

Improved upper bounds for partial spreads

, and constant dimension

On Minimum Integer Representations of Weighted Games

k=3

On the Democratic Weights of Nations

is

The Nucleolus of Large Majority Games

M=77