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  • 1
    Electronic Resource
    Electronic Resource
    Ideal secret sharing schemes with multiple secrets (1996)
    Springer
    Journal of cryptology 9 (1996), S. 233-250 
    Details
    ISSN: 1432-1378
    Keywords: Ideal secret sharing schemes ; Multiple secrets ; Matroids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider secret sharing schemes which, through an initial issuing of shares to a group of participants, permit a number of different secrets to be protected. Each secret is associated with a (potentially different) access structure and a particular secret can be reconstructed by any group of participants from its associated access structure without the need for further broadcast information. We consider ideal secret sharing schemes in this more general environment. In particular, we classify the collections of access structures that can be combined in such an ideal secret sharing scheme and we provide a general method of construction for such schemes. We also explore the extent to which the results that connect ideal secret sharing schemes to matroids can be appropriately generalized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00189262
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  • 2
    Electronic Resource
    Electronic Resource
    On Unitals ith Many Baer Sublines (1999)
    Springer
    Designs, codes and cryptography 17 (1999), S. 237-252 
    Details
    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
    URL: http://dx.doi.org/10.1023/A:1026487412101
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Triads, Flocks of Conics and Q -(5,q) (1999)
    Springer
    Designs, codes and cryptography 18 (1999), S. 63-70 
    Details
    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
    URL: http://dx.doi.org/10.1023/A:1008376900914
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Spreads and group divisible designs (1993)
    Springer
    Designs, codes and cryptography 3 (1993), S. 229-235 
    Details
    ISSN: 1573-7586
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract By removing the components of at-spread $$S$$ of a finite projective spacePG(d, q) from each hyperplane ofPG(d, q), the blocks of a regular group divisible design $$\mathcal{G}(S)$$ are obtained We characterize geometrict-spreads as thoset-spreads $$S$$ which are such that the dual of $$\mathcal{G}(S)$$ is also a group divisible design.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01388484
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  • 5
    Electronic Resource
    Electronic Resource
    Key distribution patterns using Minkowski planes (1995)
    Springer
    Designs, codes and cryptography 5 (1995), S. 261-267 
    Details
    ISSN: 1573-7586
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A key distribution pattern is a combinatorial structure which provides a secure method of distributing secret keys among a number of participants in a cryptographic scheme. Inversive and Laguerre planes have been used to construct key distribution patterns with storage requirements lower than the trivial distribution system. In this note we construct key distribution patterns from Minkowski planes, the third of the so-calledcircle geometries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01388388
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Ovoids ofPG(3, 16) are elliptic quadrics, II (1992)
    Springer
    Journal of geometry 44 (1992), S. 140-159 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a previous paper [8] the authors have shown that every ovoid ofPG(3, 16) is an elliptic quadric. The arguments used a computer and also depended on the computer-aided classification of hyperovals ofPG(2, 16) (see [3]). Recently (see [9]) the classification of hyperovals ofPG(2,16) has been obtained without the use of a computer. The present paper completes a computer-free proof that every ovoid ofPG(3,16) is an elliptic quadric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228289
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Ovoids ofPG(3, 16) are elliptic quadrics (1990)
    Springer
    Journal of geometry 38 (1990), S. 95-106 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is proved, with the aid of a computer, that in PG(3,16) the only ovoids are the elliptic quadrics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01222898
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Projective spread sets (1990)
    Springer
    Journal of geometry 37 (1990), S. 55-76 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper the notion of a spread set for at-spread ofPG(2t+1,q) is generalised and it is shown that certaint-spreads ofPG(n, q) correspond to these generalised spread sets. Then a projective spread set is defined and it is shown that anyt-spread ofPG(n, q) corresponds to a projective spread set. Connections between the spread set and the projective spread set of at-spread are discussed, in particular in the case of at-spread ofPG(2t + 1,q) the spread set and the projective spread set are equivalent, giving a new and straightforward construction of a spread set. The methods developed are used to show, with the aid of a computer, that the 1-packing ofPG(7,2) constructed by Baker is regulus-free.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230359
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  • 9
    Electronic Resource
    Electronic Resource
    Arcs fixed byA 5 andA 6 (1996)
    Springer
    Journal of geometry 55 (1996), S. 123-138 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The complete list of thek-arcsK inPG(n, q) fixed by a projective group isomorphic toA 5 orA 6, which acts primitively on the points ofK, is presented. This leads to new classes of 10-arcs inPG(n, q), 3 ≤n ≤5. Our results also show that the non-classical 10-arc inPG(4, 9), discovered by D.G. Glynn [3], belongs to an infinite class of 10-arcs inPG(4, 3h),h ≥2, fixed by a projective group isomorphic toA 6.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01223038
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  • 10
    Electronic Resource
    Electronic Resource
    A new hyperoval inPG(2, 32) (1992)
    Springer
    Journal of geometry 44 (1992), S. 117-139 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new hyperoval is constructed in the Desarguesian projective planePG(2, 32). It has a full collineation stabiliser of order 3. It is also shown, with the aid of a computer, that the collineation stabiliser of any further new hyperoval is either trivial or has order 2 with the generator fixing no point on the hyperoval.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228288
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