Centre for the Mathematics of Symmetry and Computation



Mark Ioppolo


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Mark Ioppolo


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.

Why my research is important

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.


Centre for the Mathematics of Symmetry and Computation

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Last updated:
Tuesday, 1 November, 2011 2:52 PM