### Generalised dual arcs and Veronesean surfaces, with applications to cryptography

(2009) Journal of combinatorial theory, series A. 116(3). p.684-698- abstract
- We start by defining generalised dual arcs, the motivation for defining them comes from cryptography, since they can serve as a tool to construct authentication codes and secret sharing schemes. We extend the characterisation of the tangent planes of the Veronesean surface V-2(4) in PG(5,q), q odd, described in [J.W.P. Hirschfeld, J.A. Thas, General Galois Geometries, Oxford Math. Monogr., Clarendon Press/Oxford Univ. Press, New York, 1991], as a set of q(2) + q + 1 planes in PG(5, q), such that every two intersect in a point and every three are skew. We show that a set of q 2 + q planes generating PG(5, q), q odd, and satisfying the above properties can be extended to a set of q2 + q + I planes still satisfying all conditions. This result is a natural generalisation of the fact that a q-arc in PG(2, q), q odd, can always be extended to a (q + 1)-arc. This extension result is then used to study a regular generalised dual arc with parameters (9, 5, 2, 0) in PG(9, q), q odd, where we obtain an algebraic characterisation of such an object as being the image of a cubic Veronesean.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-592357

- author
- Andreas Klein UGent, Jeroen Schillewaert UGent and Leo Storme UGent
- organization
- year
- 2009
- type
- journalArticle (original)
- publication status
- published
- subject
- journal title
- Journal of combinatorial theory, series A
- J. Combin. Theory, Ser. A
- volume
- 116
- issue
- 3
- pages
- 684 - 698
- Web of Science type
- Article
- Web of Science id
- 000264406900011
- JCR category
- MATHEMATICS
- JCR impact factor
- 0.783 (2009)
- JCR rank
- 81/251 (2009)
- JCR quartile
- 2 (2009)
- ISSN
- 0097-3165
- DOI
- 10.1016/j.jcta.2008.11.001
- language
- English
- UGent publication?
- yes
- classification
- A1
- id
- 592357
- handle
- http://hdl.handle.net/1854/LU-592357
- date created
- 2009-04-09 11:30:22
- date last changed
- 2009-04-10 14:02:45

@article{592357, abstract = {We start by defining generalised dual arcs, the motivation for defining them comes from cryptography, since they can serve as a tool to construct authentication codes and secret sharing schemes. We extend the characterisation of the tangent planes of the Veronesean surface V-2(4) in PG(5,q), q odd, described in [J.W.P. Hirschfeld, J.A. Thas, General Galois Geometries, Oxford Math. Monogr., Clarendon Press/Oxford Univ. Press, New York, 1991], as a set of q(2) + q + 1 planes in PG(5, q), such that every two intersect in a point and every three are skew. We show that a set of q 2 + q planes generating PG(5, q), q odd, and satisfying the above properties can be extended to a set of q2 + q + I planes still satisfying all conditions. This result is a natural generalisation of the fact that a q-arc in PG(2, q), q odd, can always be extended to a (q + 1)-arc. This extension result is then used to study a regular generalised dual arc with parameters (9, 5, 2, 0) in PG(9, q), q odd, where we obtain an algebraic characterisation of such an object as being the image of a cubic Veronesean.}, author = {Klein, Andreas and Schillewaert, Jeroen and Storme, Leo}, issn = {0097-3165}, journal = {Journal of combinatorial theory, series A}, language = {eng}, number = {3}, pages = {684--698}, title = {Generalised dual arcs and Veronesean surfaces, with applications to cryptography}, url = {http://dx.doi.org/10.1016/j.jcta.2008.11.001}, volume = {116}, year = {2009}, }

- Chicago
- Klein, Andreas, Jeroen Schillewaert, and Leo Storme. 2009. “Generalised Dual Arcs and Veronesean Surfaces, with Applications to Cryptography.”
*Journal of Combinatorial Theory, Series A*116 (3): 684–698. - APA
- Klein, A., Schillewaert, J., & Storme, L. (2009). Generalised dual arcs and Veronesean surfaces, with applications to cryptography.
*Journal of combinatorial theory, series A*,*116*(3), 684–698. - Vancouver
- 1.Klein A, Schillewaert J, Storme L. Generalised dual arcs and Veronesean surfaces, with applications to cryptography. Journal of combinatorial theory, series A. 2009;116(3):684–98.
- MLA
- Klein, Andreas, Jeroen Schillewaert, and Leo Storme. “Generalised Dual Arcs and Veronesean Surfaces, with Applications to Cryptography.”
*Journal of combinatorial theory, series A*116.3 (2009): 684–698. Print.