Abstract
Equations for coefficients of tactical decomposition matrices for 2-designs are well-known and they have been used for constructions of many examples of 2-designs. In this paper, we generalize these equations and propose an explicit equation system for coefficients of tactical decomposition matrices for \(t\text{-}(v,k,\lambda _t)\) designs, for any integer value of \(t.\)
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References
Dembowski P.: Finite Geometries. Springer, Berlin (1968).
Janko Z., van Trung Tran: Construction of a new symmetric block design for (78, 22, 6) with the help of tactical decompositions. J. Comb. Theory A 40, 451–455 (1985).
Kramer E.S., Mesner D.M.: \(t\)-designs on hypergraphs. Discret. Math. 15, 263–296 (1976).
Khosrovshahi G., Laue R.: \(t\)-designs with \(t\ge 3.\) In: Colbourn C.J., Dinitz J.H. (eds.) The Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton (2007).
Krčadinac V., Nakić A., Pavčević M.O.: The Kramer-Mesner method with tactical decompositions: some new unitals on \(65\) points. J. Comb. Des. 19(4), 290–303 (2011).
Mathon R., Rosa A.: \(2\text{-}(v, k,\lambda )\) designs of small order. In: Colbourn C.J., Dinitz J.H. (eds.) The Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton (2007).
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Communicated by L. Teirlinck.
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Krčadinac, V., Nakić, A. & Pavčević, M.O. Equations for coefficients of tactical decomposition matrices for \(t\)-designs. Des. Codes Cryptogr. 72, 465–469 (2014). https://doi.org/10.1007/s10623-012-9779-y
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DOI: https://doi.org/10.1007/s10623-012-9779-y