On cubic curves in projective planes of characteristic two

Australasian Journal of Combinatorics

Volumn 17, Issue , 1998, Pages 1-20

  Glynn, David G ^a  

^a UNIVERSITY OF CANTERBURY   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039413226     PISSN: 10344942     EISSN: 22023518     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. R. W. Ball, Dualities of finite projective planes, Duke Math. J. 15 (1948), 929-940.
2. A. A. Bruen and J. W. P. Hirschfeld, Intersections in projective space, II. Pencils of quadric surfaces, European J. Combin. 9 (1988), 275-286.
3. A. D. Campbell, Plane cubic curves in the Galois fields of order 2n. Ann. of Math. 27 (1926), 395-406.
4. M. Cicchese, Sulle cubiche di un piano di Galois, Rend. Mat. Pura ed Appl 24 (1965), 291-330.
5. M. Cicchese, Sulle cubiche di un piano lineare S2, q con q 1 (mod 3), Rend. Mat 4 (1971), 249-283.
6. M. Deuring, Invarianten und Normalformen elliptischer Funktionkorper, Math. Z. 47 (1940), 47-56.
7. L. E. Dickson, On the canonical forms and automorphs of ternary cubic forms, Amer. J. Math 30 (1908), 117-128.
8. L. E. Dickson, Invariantive theory of plane cubic curves modulo 2, Amer. J. Math. 37 (1915), 107-116.
9. F. Enriques and O. Chisini, Lezioni sulla teona geometrica delle equazioni e delle funzioni algebraiche, vol. I & II, Zanichelli, Bologna, 1915.
10. A. Garcia and J. F. Voloch, Duality for projective curves, Instituto de matematica pura e aplicada, Serie A, Informes de Matematica 085 (1989).
11. D. G. Glynn, Finite Projective Planes and Related Combinatorial Systems, Ph. D Thesis, University of Adelaide, South Australia, 1978.
12. D. G. Glynn, Two new sequences of ovals in finite Desarguesian planes of even order, Comb. Math. X (Adelaide 1982), Lecture Notes in Math. 1036 (1983), 217-229, Springer, Berlin, Heidelberg, New York and Tokyo.
13. D. G. Glynn, A condition for the existence of ovals in PG(2, q), q even, Geometriae Ded. 32 (1989), 247-252.
14. D. G. Glynn, On the number of points on a hypersurface in PG(n, q) and the modular counterparts of Cayley's hyperdeterminants, submitted for publication.
15. V. D. Goppa, Algebraico-geometric codes, Math. USSR Izvestiya 21 (1983), 75-91.
16. M. Hall, Jr., Ovals in the Desarguesian plane of order 16, Ann. di Mat. Pura ed Appl. 102 (1975), 159-176.
17. R. W. Hartley, Determination of the ternary collineation groups whose coefficients lie in the GF(2n), Ann. Math. (2) 2 (1926), 140-158.
18. R. Hartshorne, Algebraic Geometry, Graduate Texts in Maths, 52, Springer, New York, Heidelberg, Berlin, 1983.
19. J. W. P. Hirschfeld, Projective Geometries over Finite Fields, Oxford Uni. Press, Oxford, 1979.
20. J. W. P. Hirschfeld, Linear codes and algebraic curves, Geometrical Combinatorics §4, (eds. F. C. Holroyd & R. J. Wilson), Pitman, Research Notes in Mathematics 114 (1984), 35-53.
21. J. W. P. Hirschfeld and J. F. Voloch, The characterization of elliptic curves over finite fields, J. Austral. Math. Soc. (Series A) 45 (1988), 275-286.
22. L. Lunelli and M. See, k-archi completi nei piani proiettivi desarguesiani di rango 8 e 16, Politecnico Milano, Centro Caleol. Numerici (1958), 1-15.
23. R. Schoof, Non-singular plane cubic curves over finite fields, PhD thesis, Dni. of Amsterdam, 1985.
24. B. Segre, Bulle ovali nei piani lineari finiti, Atti Accad. Naz. Lineei Rend 17 (1954), 1-2.
25. B. Segre, Intorno alia geometria sopra un campo di caratteristica due, Istanbul Dni. Fen Fakueltesi Meemnasi, Seri A Sidi ve Talbiki Matematik 21 (1956), 97-123.
26. B. Segre, Le geometrie di Galois, Ann. Mat. Pura Appl 48 (1959), 1-97.
27. B. Segre, Arithmetische Eigenschaften von Galois-Riiumen. I, Math. Annalen 154 (1964), 195-256.
28. J. G. Semple and L. Roth, Introduction to Algebraic Geometry, Clarendon Press, Oxford, 1985.
29. J. H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Maths, 106, Springer, New York, Berlin, Heidelberg, Tokyo, 1986.
30. J. F. Voloeh, On the completeness of certain plane arcs, European J. Combinatorics 8 (1987), 453-456.
31. J. F. Voloeh, A note on elliptic curves over finite fields, Bull. Soc. math. France 116 (1988), 455-458.
32. J. F. Voloeh, On the completeness of certain plane arcs II, European J. Combinatorics 11 (1990), 491-496.
33. W. C. Waterhouse, Abelian varieties over finite fields, Ann. Sci. Ecole Norm. Sup. 2 (1969), 521-560.