nach oben

Designs, Codes and Cryptography

Erschienen in:

01.10.2016

A note on relative hemisystems of Hermitian generalised quadrangles

verfasst von: John Bamberg, Melissa Lee, Eric Swartz

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1/2016

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space \({\mathrm {H}}(3,q^2)\), unifying all known infinite families. We use these conditions to provide new proofs of the existence of the known infinite families of relative hemisystems. Reproving these results has allowed us to find new relative hemisystems closely related to an infinite family of Cossidente’s, and develop techniques that are likely to be useful in finding relative hemisystems in future.

Vorheriger Artikel Separating invertible key derivations from non-invertible ones: sequential indifferentiability of 3-round Even–Mansour

Nächster Artikel New infinite series of 2-designs over the binary and ternary field

Aguglia A., Giuzzi L.: Intersections of the Hermitian surface with irreducible quadrics in even characteristic. ArXiv e-prints arXiv:1407.8498.

Bayens L.: Hyperovals, Laguerre planes and hemisystems—an approach via symmetry. ProQuest LLC, Ann Arbor, MI. Ph.D. Thesis, Colorado State University (2013).

Buekenhout F.: Handbook of Incidence Geometry: Buildings and Foundations. North Holland, Amsterdam (1995).

Cossidente A.: A new family of relative hemisystems on the hermitian surface. Des. Codes Cryptogr. 75, 213–221 (2013).

Cossidente A.: Relative hemisystems on the Hermitian surface. J. Algebr. Comb. 38(2), 275–284 (2013).

Cossidente A., Pavese F.: Intriguing sets of \({\cal W}(5, q)\) even. J. Comb. Theory. A 127, 303–313 (2014).

Cossidente A., Penttila T.: Hemisystems on the hermitian surface. J. Lond. Math. Soc. 72(3), 731–741 (2005).

Dixon J.D., Mortimer B.: Permutation groups. Graduate Texts in Mathematics, vol. 163. Springer, New York (1996).

The GAP Group: GAP—Groups, Algorithms, and Programming, version 4.7.5 (2014).

10.

Gurobi Optimization, Inc.: Gurobi Optimizer Reference Manual (2015).

11.

Hirschfeld J.W.P., Thas J.A.: General Galois geometries. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York. Oxford Science Publications (1991).

12.

Kleidman P.B., Liebeck M.W.: The Subgroup Structure of the Finite Classical Groups, vol. 129. Cambridge University Press, Cambridge (1990).

13.

Martis M., Bamberg J., Morris S.: An enumeration of certain projective ternary two-weight codes and their relationship to the cubic Segre variety. J. Comb. Des. arXiv:1406.6748v1.

14.

Payne S.E., Thas J.A.: Finite Generalized Quadrangles, vol. 110. European Mathematical Society, Zürich (2009).

15.

Penttila T., Williford J.: New families of \(Q\)-polynomial association schemes. J. Comb. Theory A 118(2), 502–509 (2011).

16.

Segre B.: Forme e geometrie hermitiane, con particolare riguardo al caso finito. Ann. Mat. Pura Appl. 4(70), 1–201 (1965).

17.

van Dam E.R., Martin W.J., Muzychuk M.: Uniformity in association schemes and coherent configurations: cometric Q-antipodal schemes and linked systems. J. Comb. Theory. A 120(7), 1401–1439 (2013).

18.

Wilson R.: The Finite Simple Groups, vol. 251. Springer, London (2009).

Titel: A note on relative hemisystems of Hermitian generalised quadrangles
verfasst von: John Bamberg
Melissa Lee
Eric Swartz
Publikationsdatum: 01.10.2016
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1/2016
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-015-0135-x

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Weitere Artikel der Ausgabe 1/2016

Complete weight enumerators of some linear codes and their applications

Two classes of cyclic codes and their weight enumerator

homomorphic hash functions: worst case to average case reduction and short collision search

New infinite series of 2-designs over the binary and ternary field

A reduction of Semigroup DLP to classic DLP

Policy-based signature scheme from lattices