caa a22 4500 475807316 CHVBK 20180406123750.0 cr unu---uuuuu 170329e20000401xx s 000 0 eng 10.1023/A:1008371502105 doi (NATIONALLICENCE)springer-10.1023/A:1008371502105 McQuillan James Department of Mathematics, Middlesex College, The University of Western Ontario, London, N6A 5B7, Ontario, Canada aut Pencils of Hyperconics in Projective Planes of Characteristic Two [Elektronische Daten] [James McQuillan] Let F be any field, finite or infinite, of characteristic 2. Put Π=PG(2,F). Let H 1,H 2 be hyperconics in Π. In this note we study the intersectionH 1∩ H 2. In particular we obtain canonical forms for H 1,H 2 in the cases where |H 1∩ H 2|=4,5,6. One interesting consequence is that the case |H 1∩ H 2|=6 can only occur if F contains a subfield of order 4. Related results concerning "pencils of hyperconics” are presented in Theorems 6 through 9. This work also leads to an extension to general fields of characteristic 2 of the well-known even intersection property for hyperovals in PG(2,4) which is pursued elsewhere ([2]). Kluwer Academic Publishers, 2000 pencil of conics nationallicence PG(2,4)subplane nationallicence hexads nationallicence Designs, Codes and Cryptography Kluwer Academic Publishers 20/1(2000-04-01), 65-71 0925-1022 20:1<65 2000 20 10623 https://doi.org/10.1023/A:1008371502105 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008371502105 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- McQuillan James Department of Mathematics, Middlesex College, The University of Western Ontario, London, N6A 5B7, Ontario, Canada aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 20/1(2000-04-01), 65-71 0925-1022 20:1<65 2000 20 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer