## On designs related to coherent configurations of type $$(^ 2\;^ 2_ 4)$$.(English)Zbl 0756.05013

Coherent configurations were earlier studied by D. G. Higman [Linear Algebra Appl. 93, 209-239 (1987; Zbl 0618.05014)]. The parametric relations for the coherent configurations of type $$\left({2\atop\;}{2\atop n}\right)$$ and related designs are established here. It is shown that the Witt design $${\mathcal S}(5,8,24)$$ is determined by the association scheme on its blocks and the family of designs based on systems of linked symmetric designs is characterized.
Reviewer: K.Sinha (Ranchi)

### MSC:

 05B05 Combinatorial aspects of block designs 05B30 Other designs, configurations 05E30 Association schemes, strongly regular graphs

Zbl 0618.05014
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### References:

 [1] Assmus, E.F.; Mattson, H.F., New 5-designs, J. combin. theory, 6, 122-151, (1969) · Zbl 0179.02901 [2] Baranyai, Z., On factorization of the complete uniform hypergraphs, (), 99-108 [3] Beker, H.; Haemers, W., 2-designs having an intersection number k − n, J. combin. theory ser. A, 28, 64-81, (1980) · Zbl 0425.05009 [4] Brouwer, A.E., Some unitals on 28 points and their embeddings in projective planes of order 9, Math. centre report ZW, 102, (February 1981) [5] Brouwer, A.E., The uniqueness of the near hexagon on 759 points, (), 47-60 · Zbl 0448.05020 [6] Cameron, P.J., On groups with several doubly transitive permutation representations, Math. Z., 128, 1-14, (1972) · Zbl 0227.20001 [7] Cameron, P.J.; Goethals, J.M.; Seidel, J.J., The Krein condition, spherical designs, norton algebras, and permutation groups, Proc. kon. nederl. akad. wet. A, 81, 196-206, (1978) · Zbl 0408.05016 [8] Cameron, P.J.; van Lint, J.H., Graphs, codes and designs, () · Zbl 0427.05001 [9] Dembowski, P., Finite geometries, (1968), Springer Berlin · Zbl 0159.50001 [10] Higman, D.G., Coherent algebras, Linear algebra appl., 93, 209-239, (1987) · Zbl 0618.05014 [11] D.G. Higman, Coherent algebras of dimension 4, preprint. [12] Higman, D.G., Coherent configurations I: ordinary representation theory, Geom. dedicata, 4, 1-32, (1975) · Zbl 0333.05010 [13] Hobart, S.A., A characterization of t-designs in terms of the inner distribution, European J. combin., 10, 445-448, (1989) · Zbl 0679.05007 [14] Hughes, D.R.; Piper, F.C., Design theory, (1985), Cambridge Univ. Press Cambridge · Zbl 0561.05009 [15] Mathon, R., 3-class association schemes, (), 123-155, Congr. Numer. XIII. [16] Ray-Chaudhuri, D.K.; Wilson, R.M., The existence of resolvable block designs, (), 361-375
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