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Paper   IPM / M / 7403
School of Mathematics
  Title:   Enumeration of t-designs through intersection matrices
  Author(s): 
1.  M. Mohammad-Noori
2.  Z. Eslami
3.  G. B. Khosrovshahi
  Status:   Published
  Journal: Des. Codes Cryptogr.
  Vol.:  32
  Year:  2004
  Pages:   185-191
  Supported by:  IPM
  Abstract:
In this paper, we exploit some intersection matrices to empower a backtracking approach based on Kramer-Menser 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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