论文信息 - On Unitals ith Many Baer Sublines

On Unitals ith Many Baer Sublines

AbstractWe identify the points of PG(2, q) ith the directions of lines in GF(q3), viewed as a 3-dimensional affine space over GF(q). Within this frameork we associate to a unital in PG(2, q) a certain polynomial in to variables, and show that the combinatorial properties of the unital force certain restrictions on the coefficients of this polynomial. In particular, if q = p2 where p is prime then e show that a unital is classical if and only if at least (q - 2) $$\sqrt q$$ secant lines meet it in the points of a Baer subline.

Aart Blokhuis | Simeon Ball | Christine M. O'Keefe

[1] Rudolf Metz. On a class of unitals , 1979 .

[2] F. Buekenhout. Existence of unitals in finite translation planes of order q2 with a kernel of order q , 1976 .

[3] Christiane Lefevre-Percsy. Characterization of Buekenhout-Metz unitals , 1981 .

[4] G. Korchmáros,et al. A Graphic Characterization of Hermitian Curves , 1983 .

[5] C. T. Quinn,et al. Concerning a characterisation of Buekenhout-Metz unitals , 1995 .

[6] Tim Penttila,et al. Characterizations of Buekenhout-Metz unitals , 1996 .

[7] Tim Penttila,et al. Sets of type (m, n) in the affine and projective planes of order nine , 1995, Des. Codes Cryptogr..

[8] L. Rédei,et al. Lückenhafte Polynome über endlichen Körpern , 1970 .

[9] J. Thas,et al. A characterization of Hermitian curves , 1991 .

[10] J. Hirschfeld. Projective Geometries Over Finite Fields , 1980 .