Codes Based on Complete Graphs View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1996

AUTHORS

Dieter Jungnickel , Marialuisa J. De Resmini , Scott A. Vanstone

ABSTRACT

We consider the problem of embedding the even graphical code based on the complete graph on n vertices into a shortening of a Hamming code of length 2m - 1, where m = h(n) should be as small as possible. As it turns out, this problem is equivalent to the existence problem for optimal codes with minimum distance 5, and optimal embeddings can always be realized as graphical codes based on Kn. As a consequence, we are able to determine h(n) exactly for all n of the form 2k + 1 and to narrow down the possibilities in general to two or three conceivable values. More... »

PAGES

159-165

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4613-1395-3_11

DOI

http://dx.doi.org/10.1007/978-1-4613-1395-3_11

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1021658850


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