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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Designs, codes and cryptography 17 (1999), S. 237-252 
    ISSN: 1573-7586
    Keywords: unital ; Hermitian curve
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We identify the points of PG(2, q) ith the directions of lines in GF(q 3), 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 = p 2 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.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Designs, codes and cryptography 18 (1999), S. 63-70 
    ISSN: 1573-7586
    Keywords: Ovoids ; Flocks of Conics ; Generalized Quadrangles
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show that if an ovoid of Q (4,q),q even, admits a flock of conics then that flock must be linear. It follows that an ovoid of PG (3,q),q even, which admits a flock of conics must be an elliptic quadric. This latter result is used to give a characterisation of the classical example Q -(5,q) among the generalized quadrangles T 3( $$O$$ ), where $$O$$ is an ovoid of PG (3q) and q is even, in terms of the geometric configuration of the centres of certain triads.
    Type of Medium: Electronic Resource
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