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Small complete caps in PG(r,q), r ⩾ 3

✍ Scribed by Giorgio Faina; Fernanda Pambianco

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
278 KB
Volume
174
Category
Article
ISSN
0012-365X

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✦ Synopsis

A very difficult problem for complete caps in PG(r,q) is to determine their minimum size. The results on this topic are still scarce and in this paper we survey the best results now known. Furthermore, we construct new interesting sporadic examples of complete caps in PG(3, q) and in PG(4, q) such that their size are smaller than the currently known. As a consequence, we get that the Pellegrino's conjecture on the minimal size of a complete k-cap in PG(3,q), q odd, is in general false.

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## Abstract Some new families of small complete caps in __PG__(__N, q__), __q__ even, are described. By using inductive arguments, the problem of the construction of small complete caps in projective spaces of arbitrary dimensions is reduced to the same problem in the plane. The caps constructed in