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Erschienen in: Designs, Codes and Cryptography 2/2014

01.08.2014

Equations for coefficients of tactical decomposition matrices for \(t\)-designs

verfasst von: Vedran Krčadinac, Anamari Nakić, Mario Osvin Pavčević

Erschienen in: Designs, Codes and Cryptography | Ausgabe 2/2014

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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 \(t.\)
Literatur
1.
Zurück zum Zitat Dembowski P.: Finite Geometries. Springer, Berlin (1968). Dembowski P.: Finite Geometries. Springer, Berlin (1968).
2.
Zurück zum Zitat 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). 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).
3.
Zurück zum Zitat Kramer E.S., Mesner D.M.: \(t\)-designs on hypergraphs. Discret. Math. 15, 263–296 (1976). Kramer E.S., Mesner D.M.: \(t\)-designs on hypergraphs. Discret. Math. 15, 263–296 (1976).
4.
Zurück zum Zitat 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). 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).
5.
Zurück zum Zitat 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). 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).
6.
Zurück zum Zitat 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). 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).
Metadaten
Titel
Equations for coefficients of tactical decomposition matrices for -designs
verfasst von
Vedran Krčadinac
Anamari Nakić
Mario Osvin Pavčević
Publikationsdatum
01.08.2014
Verlag
Springer US
Erschienen in
Designs, Codes and Cryptography / Ausgabe 2/2014
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-012-9779-y

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