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SEMINAR: Groups and Combinatorics Seminars

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Groups and Combinatorics Seminar

Neil Gillespie (UWA)

will speak on

Completely regular codes with large minimum distance


Daniel Hawtin (UWA) will speak on Elusive Codes in Hamming Graphs

at 1pm Tuesday 4th of December in MLR2


Completely regular codes with large minimum distance: In 1973 Delsarte introduced completely regular codes as a generalisation of perfect codes. Not only are completely regular codes of interest to coding theorists due to their nice regularity properties, but they also characterise certain families of distance regular graphs. Although no complete classification of these codes is known, there have been several attempts to classify various subfamilies. For example, Borges, Rifa and Zinoviev classified all binary non-antipodal completely regular codes. Similarly, in joint work with Praeger, we characterised particular families of completely regular codes by their length and minimum distance, and additionally with Giudici, we also classified a family of completely transitive codes, which are necessarily completely regular. In this work with Praeger, and also with Giudici, the classification given by Borges, Rifa and Zinoviev was critical to the final result. However, recently Rifa and Zinoviev constructed an infinite family of non-antipodal completely regular codes that does not appear in their classification. This, in particular, led to a degree of uncertainty about the results with Praeger and with Giudici. In this talk I demonstrate how I overcame this uncertainty by classifying all binary completely regular codes of length m and minimum distance $ elta$ such that $ elta>m/2$.

Elusive Codes in Hamming Graphs:

We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We provide an infinite family of elusive pairs, where the group in question acts transitively on the set of neighbours of the code. In our examples, we find that the alphabet size always divides the length of the code, and prove that there is no elusive pair for the smallest set of parameters for which this is not the case.
Speaker(s) Neil Gillespie and Daniel Hawtin
Location Maths Lecture Room 2
Contact Michael Giudici <[email protected]>
Start Tue, 04 Dec 2012 13:00
End Tue, 04 Dec 2012 13:45
Submitted by Michael Giudici <[email protected]>
Last Updated Mon, 03 Dec 2012 07:42
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