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Perfect codes in the graphs Ok and L(Ok)

Published online by Cambridge University Press:  18 May 2009

D. H. Smith
D. H. Smith
Affiliation:
Polytechnic of Wales, Pontypridd, Wales
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In [6] the question of the existence of perfect e-codes in the infinite family of distance-transitive graphs Ok was considered. It was pointed out that it is difficult to rule out completely any particular value of e because of the difficulty of working with the sphere packing condition. For e= 1, 2, 3 it can be seen from the results of [6] that the condition given by the generalisation of Lloyd's theorem is satisfied for infinitely many values of k. We shall show that this is not the case for e=4 and we shall prove that there are no perfect 4-codes in Ok.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 169 - 172
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

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