On extendable planes, M.D.S. codes and hyperovals in PG(2, q), q=2t View Full Text


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Article Info

DATE

1988-10

AUTHORS

Aiden A. Bruen, Robert Silverman

ABSTRACT

The question of the existence of finite planes seems to be beyond the range of present techniques. In this paper we skirmish with an easier question: extendable planes. We show how extendable planes arise as special cases of certain maximum distance separable codes (M.D.S. codes). A synthetic characterization of extendable planes is obtained. A different characterization is obtained in terms of hyperoval systems. Moreover, since π=PG(2, q), q=2t, is extendable this leads to new insights concerning the subtle and marvellous structure of certain hyperoval systems in π. A priori, it seems somewhat surprising that very much can be said about hyperovals in π, as they have certainly not been classified. In particular, we obtain a partial generalization of the famous ‘even intersection’ property of hyperovals in PG(2, 4). We conclude with a discussion of hyperoval ‘spreads’ and ‘packings’ in π along with some open questions. More... »

PAGES

31-43

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00147798

DOI

http://dx.doi.org/10.1007/bf00147798

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1025324460


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