The main topics in our proposed research work "Combinatorial constructions under group actions" will be:
1. Matroids and codes: There are interesting connections between linear codes over GF(2) of GF(3) and binary,
ternary or regular matrix matroids. Especially the isometry classes of these codes correspond to the isomorphism
classes of the matroids. Since we have already computed complete lists of representatives of linear codes we have
complete lists of representatives of these matroids which now can be tested for certain properties.
2. Combinatorial species theory: This branch of combinatorial mathematics dealing with the enumeration of both
labelled and unlabelled structures was mainly developed in Canada during the last 15 years. Many parts of this
theory could be reformulated in order to get algorithms rather for constructing these objects than for enumerating
them. It is planned to develop a data structure for constructive species theory in a public domain computer algebra
system and to implement the standard objects and standard operations of species theory.