nach oben

Designs, Codes and Cryptography

Erschienen in:

26.10.2017

Flag-transitive point-quasiprimitive 2-\((v,\, k,\, 2)\) designs

verfasst von: Zhilin Zhang, Shenglin Zhou

Erschienen in: Designs, Codes and Cryptography | Ausgabe 9/2018

Einloggen, um Zugang zu erhalten

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

search-config

KI-gestützte Suche

Aus

Abstract

Let \(\mathcal {D}\) be a non-trivial 2-\((v,\,k,\,2)\) design. Assume that G is a flag-transitive and point-quasiprimitive automorphism group of \(\mathcal {D},\) then G is of holomorph affine or almost simple type.

Vorheriger Artikel On critical exponents of Dowling matroids

Nächster Artikel On the number of inequivalent Gabidulin codes

Camina A.R., Praeger C.E.: Line-transitive, point quasiprimitive automorphism groups of finite linear spaces are affine or almost simple. Aequ. Math. 61, 221–232 (2001).MathSciNetCrossRefMATH

Colburn C.J., Dinitz J.H. (eds.): Handbook of Combinatorial Designs. Discrete Mathematics and Its Applications (Boca Raton), 2nd edn. Chapman and Hall/CRC, Boca Raton (2007).

Davies H.: Flag-transitivity and primitivity. Discret. Math. 63, 91–93 (1987).MathSciNetCrossRefMATH

Dembowski P.: Finite Geometries. Springer, New York (1968).CrossRefMATH

Dixon J.D., Mortimer B.: The primitive permutation groups of degree less than 1000. Math. Proc. Camb. Philos. Soc. 103, 213–238 (1988).MathSciNetCrossRefMATH

Fang W., Dong H., Zhou S.: Flag-transitive 2-\((v, k, 4)\) symmetric designs. Ars Comb. 95, 333–342 (2010).MathSciNetMATH

Kantor W.: Primitive permutation groups of odd degree, and an application to finite projective planes. J. Algebra 106, 15–45 (1987).MathSciNetCrossRefMATH

Liang H., Zhou S.: Flag-transitive point-primitive automorphism groups of nonsymmetric 2-\((v, k, 2)\) designs. J. Comb. Des. 24(8), 421–435 (2016).MathSciNetCrossRefMATH

Liebeck M.W., Praeger C.E., Saxl J.: On the O’Nan-Scott theorem for finite primitive permutation groups. J. Aust. Math. Soc. A 44, 389–396 (1988).MathSciNetCrossRefMATH

10.

O’Reilly Regueiro E.: On primitivity and reduction for flag-transitive symmetric designs. J. Comb. Theory A 109(1), 135–148 (2005).MathSciNetCrossRefMATH

11.

O’Reilly Regueiro E.: Reduction for primitive flag-transitive \((v, \,k,\,4)\)-symmetric designs. Des. Codes Cryptogr. 56, 61–63 (2010).MathSciNetCrossRefMATH

12.

Praeger C.E.: Finite quasiprimitive graphs. In: Surveys in Combinatorics, 1997 (London). London Mathematical Society Lecture Notes Series, vol. 241, pp. 65–85. Cambridge University Press, Cambridge (1997).

13.

Praeger C.E.: An O’Nan-Scott theorem for finite quaprimitive permutation groups and an application to 2-arc transitive graphs. J. Lond. Math. Soc. 47(2), 227–239 (1993).CrossRefMATH

14.

Tian D., Zhou S.: Flag-transitive point-primitive symmetric \((v, \,k, \,\lambda )\) designs with \(\lambda \) at most 100. J. Comb. Des. 21, 127–141 (2013).MathSciNetCrossRefMATH

15.

Zieschang P.-H.: Flag transitive automorphism groups of 2-designs with \((r,\, \lambda )=1\). J. Algebra 118, 265–275 (1988).MathSciNet

Titel: Flag-transitive point-quasiprimitive 2- designs
verfasst von: Zhilin Zhang
Shenglin Zhou
Publikationsdatum: 26.10.2017
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 9/2018
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0432-7

Springer Professional

Abstract

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

Weitere Artikel der Ausgabe 9/2018

On critical exponents of Dowling matroids

Flags of almost affine codes and the two-party wire-tap channel of type II

Solving a class of modular polynomial equations and its relation to modular inversion hidden number problem and inversive congruential generator

On the number of inequivalent Gabidulin codes

Improved cryptanalysis of rank metric schemes based on Gabidulin codes

Duality of codes supported on regular lattices, with an application to enumerative combinatorics