Ali Reza Rahimipour

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In this paper we present a design construction from primitive permutation representations of a finite simple group G. The group G acts primitively on
the points and transitively on the blocks of the design. The construction has this property that with some conditions we can obtain t-design for t >=2. We examine our design for fourteen sporadic simple groups. As a result we found a 2-(176,5,4) design with full automorphism group M22.


primitive permutation; group; finite simple group; automorphism group

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W. Bosma and J. J. Cannon: Handbook of Magma functions. School of Mathematics and Statistics, University of Sydney, Sydney (1995).

P. J. Cameron and A. Rudvalis: A design and a geometry for the group Fi 22 . Des. Codes Cryptogr. 44 (2007), no. 1-3, 11-14.

P. J. Cameron and J. H. van Lint: Designs, Graphs, Codes and their Links. Cambridge University Press, 1991.

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson: An Atlas of Finite Groups. Oxford: Oxford University Press, 1985.

D. Crnkovi´ c, V. Mikuli´ c and B. G. Rodrigues: Designs, strongly regular graphs and codes constructed from some primitive groups. In Information Security, Coding Theory and Related Combinatorics (D. Crnkovic & V. Tonchev, Eds.), IOS Press, Amsterdam, 2011, pages 231-252.

J.D. Dixon and B. Mortimer: Permutation Groups. Graduate Texts in Mathematics 163, Springer-Verlag, New York, 1996.

M.S. Ganief: 2-Generations of the Sporadic Simple Groups. PhD Thesis, University of Natal, 1997.

W.H. Haemers, C. Parker, V. Pless and V. D. Tonchev: A design and a code invariant under the simple group Co 3 . J. Combin. Theory Ser. A, 62 (2) (1993), 225-233.

I.M. Isaacs: Character Theory of Finite Groups. Academic Press, San Diego, 1976.

J.D. Key and J. Moori: Designs, codes and graphs from the Janko groups J 1 and J 2 . J. Combin. Math. and Combin. Comput., 40 (2002), 143-159.

J. Moori: Finite groups, designs and codes. Information security, coding theory and related combinatorics, 202-230, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 29, IOS, Am- sterdam, 2011.

J. Moori and B. G. Rodrigues: Some designs and codes invariant under the simple group Co 2 . J. of Algerbra, 316 (2007), 649-661.

J. Moori and B. G. Rodrigues: On some designs and codes invariant under the Higman-Sims group. Util. Math. 86 (2011), 225-239.

The GAP Team: GAP - Groups, Algorithms, and Programming. Version 4.5.5, 2012, (http://www.gap-system.org).

DOI: https://doi.org/10.22190/FUMI1904771R


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