- A/Prof John Bamberg
- A/Prof Alice Devillers
- W/Prof Cheryl Praeger

Neighbour-transitive codes and configurations in Johnson and q-Johnson schemes

Linear codes afford efficient mechanisms to control errors in data transmission. It is often fruitful to view a code as a subset of vertices in a graph, where each individual vertex is thought of as a codeword. My research involves the study of neighbour-transitive codes in Johnson graphs. Such codes posses a local transitivity requirement which ensures certain desirable symmetries are present in the neighbouring vertices of the code.

Association schemes capture all essential relationships between the codewords of a linear code. In design theory an important class of association schemes are the Johnson schemes. Designs can be viewed as a code in particular Johnson schemes, and in the more general q-Johnson schemes. The analogous codes are called Delsarte T-designs.

The main goals of my research are to:

1. Determine the neighbour-transitive codes in Johnson graphs.

2. Classify and construct new configurations for the Johnson and q-Johnson schemes.

3. Construct and classify Delsarte T-designs of q-Johnson schemes.

It is hoped that the study of neighbour-transitive codes will identify families of codes with large minimum distance. Such codes are useful for error detection and correction in data transmission. Johnson and q-Johnson schemes have applications in experimental design and computer science. This research will also have important implications in algebraic combinatorics and incidence geometry.