Showing papers by "J. W. P. Hirschfeld published in 1980"
Book•
24 Jan 1980
TL;DR: The first properties of the plane can be found in this article, where the authors define the following properties: 1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. Ovals 9. Arithmetic of arcs of degree two 10. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes 15.
Abstract: 1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. First properties of the plane 8. Ovals 9. Arithmetic of arcs of degree two 10. Arcs in ovals 11. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes Appendix Notation References
1,593 citations
42 citations
TL;DR: To characterize Hermitian varieties in projective space PG(d, q) of d dimensions over the Galois field GF(q), it is necessary to find those subsets K for which there exists a fixed integer n satisfying every line meets K in 1, n or q + 1 points.
22 citations
20 citations
TL;DR: The question is the range of values that lflil can take between the limits given by (2) and a precise answer is given for 2 ~.
8 citations