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Block-transitive designs in affine spaces

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Abstract

This paper deals with block-transitive t-(v, k, λ) designs in affine spaces for large t, with a focus on the important index λ = 1 case. We prove that there are no non-trivial 5-(v, k, 1) designs admitting a block-transitive group of automorphisms that is of affine type. Moreover, we show that the corresponding non-existence result holds for 4-(v, k, 1) designs, except possibly when the group is 1-D affine. Our approach involves a consideration of the finite 2-homogeneous affine permutation groups.

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Authors and Affiliations

  1. Wilhelm Schickard Institute for Computer Science, University of Tuebingen, Sand 13, 72076, Tuebingen, Germany

    Michael Huber

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  1. Michael Huber
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Correspondence to Michael Huber.

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Communicated by Ron Mullin/Rainer Steinwandt.

To Spyros Magliveras on the occasion of his 70th birthday.

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Huber, M. Block-transitive designs in affine spaces. Des. Codes Cryptogr. 55, 235–242 (2010). https://doi.org/10.1007/s10623-009-9338-3

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  • DOI: https://doi.org/10.1007/s10623-009-9338-3

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