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Enumeration of t-Designs Through Intersection Matrices

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Abstract

In this paper, we exploit some intersection matrices to empower a backtracking approach based on Kramer–Mesner matrices. As an application, we consider the interesting family of simple t-(t + 8,t + 2,4) designs, 1 ≤ t ≤ 4, and provide a complete classification for t = 1,4, as well as a classification of all non-rigid designs for t = 2,3. We also enumerate all rigid designs for t = 2. The computations confirm the results obtained in Denny and Mathon [4] through the new approach which is much simpler. Finally a list of other designs constructed by this method is provided.

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Authors and Affiliations

  1. Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran

    Z. Eslami, G. B. Khosrovshahi & M. M. Noori

  2. Department of Mathematics, University of Tehran, Tehran, Iran

    G. B. Khosrovshahi & M. M. Noori

Authors
  1. Z. Eslami
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  2. G. B. Khosrovshahi
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  3. M. M. Noori
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Eslami, Z., Khosrovshahi, G.B. & Noori, M.M. Enumeration of t-Designs Through Intersection Matrices. Designs, Codes and Cryptography 32, 185–191 (2004). https://doi.org/10.1023/B:DESI.0000029221.98300.04

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  • DOI: https://doi.org/10.1023/B:DESI.0000029221.98300.04

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