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The nonexistence of code words of weight 16 in a projective plane of order 10

โœ Scribed by C.W.H Lam; L Thiel; S Swiercz


Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
388 KB
Volume
42
Category
Article
ISSN
0097-3165

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๐Ÿ“œ SIMILAR VOLUMES


The nonexistence of ovals in a projectiv
โœ C.W.H. Lam; L. Thiel; S. Swiercz; J. McKay ๐Ÿ“‚ Article ๐Ÿ“… 1983 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 325 KB

This paper reports the result of a computer search which show s that there is no oval in a projective plane of order 10. It gives a brief description of the search method as well as a brief survey of other possible configurations in a plane of order 10.

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## Abstract In this article, we prove that there does not exist a symmetric transversal design ${\rm STD}\_2[12;6]$ which admits an automorphism group of order 4 acting semiregularly on the point set and the block set. We use an orbit theorem for symmetric transversal designs to prove our result. A

Hyperovals in the known projective plane
โœ Tim Penttila; Gordon F. Royle; Michael K. Simpson ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 382 KB

We construct by computer all of the hyperovals in the 22 known projective planes of order 16. Our most interesting result is that four of the planes contain no hyperovals, thus providing counterexamples to the old conjecture that every finite projective plane contains an oval.

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โœ R.C. Bose; S.S. Shrikhande ๐Ÿ“‚ Article ๐Ÿ“… 1973 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 729 KB

A configuration D with parameters (u, b, r. k) is an incidence structure t P, B. 2 L where ? is a set of u "points'\*, 8 is a set of b '"blocks" and 7 is an 'incidence relation" between points and blocks such that each point is incident with t blocks, and each blok is incident with Fc points. A bloc