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
and
Daniel Hawtin (UWA) will speak on
Elusive Codes in Hamming Graphs
at 1pm Tuesday 4th of December in MLR2
Abstracts:
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
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Location |
Maths Lecture Room 2
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Contact |
Michael Giudici
<[email protected]>
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Start |
Tue, 04 Dec 2012 13:00
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End |
Tue, 04 Dec 2012 13:45
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Submitted by |
Michael Giudici <[email protected]>
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Last Updated |
Mon, 03 Dec 2012 07:42
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