Existence on Splitting-Balanced Block Designs with Resolvability

1. Abel, R.J.R., Colbourn, C.J., Dinitz, J.H.: Mutually orthogonal Latin squares (MOLS). In: Colbourn, C.J., Dinitz, J.H. (eds.) The CRC Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton, pp. 160–193 (2007)

2. Abel, R.J.R., Ge, G., Yin, J.: Resolvable and near-resolvable designs. In: Colbourn, C.J., Dinitz, J.H. (eds.) The CRC Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton, pp. 124–132 (2007)

3. Abel, R.J.R., Finizo, N.J., Greig, M., Lewis, S.J.: Generalized whist tournament designs. Discrete Math. 268, 1–19 (2003)

   Article  MathSciNet  MATH  Google Scholar 

4. Anderson, I., Finizio, N.J.: Whist tournament. In: Colbourn, C.J., Dinitz, J.H. (eds.) The CRC Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton, pp. 663–668 (2007)

5. Bose, R.C.: A note on the resolvability of balanced incomplete block designs. Sankhy\(\bar{\text{a}}\) 6, 105–110 (1942)

6. Chee, Y.M., Zhang, X., Zhang, H.: Infinite families of optimal splitting authentication codes secure against spoofing attacks of higher order. Adv. Math. Commun. 5, 59–68 (2011)

   Article  MathSciNet  MATH  Google Scholar 

7. Du, B.: Splitting balanced incomplete block designs. Australas. J. Combin. 31, 287–298 (2005)

   MathSciNet  MATH  Google Scholar 

8. Du, B.: Splitting balanced incomplete block designs with block size \(3\times 2\). J. Combin. Des. 12, 404–420 (2004)

   Article  MathSciNet  MATH  Google Scholar 

9. Ge, G., Miao, Y.: PBDs, frames, and resolvability.: In: Colbourn, C.J., Dinitz, J.H. (eds.) The CRC Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton, pp. 261–265 (2007)

10. Ge, G., Miao, Y., Wang, L.: Combinatorial constructions for authentication codes. SIAM J. Discrete Math. 18, 663–678 (2005)

    Article  MathSciNet  MATH  Google Scholar 

11. Greig, M., Haanpää, H., Kaski, P.: On the coexistence of conference matrices and near resolvable 2-(\(2k+1,k,k-1\)) designs. J. Combin. Theory A 113, 703–711 (2006)

12. Huang, Q.X.: On the decomposition of \(K_n\) into complete \(m\)-partite graphs. J. Graph Theory 15, 1–6 (1991)

    Article  MathSciNet  Google Scholar 

13. Huang, Q.X.: Complete \(m\)-partite decompositions of complete multigraphs. Ars Combin. 43, 232–234 (1996)

    MathSciNet  MATH  Google Scholar 

14. Ionin, Y.J., Kharaghani, H.: Balanced generalized weighning matrices and conference matrices.: In: Colbourn, C.J., Dinitz, J.H. (eds.) The CRC Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton, pp. 306–313 (2007)

15. Kageyama, S.: An improved inequality for balanced incomplete block designs. Ann. Math. Stat. 42, 1448–1449 (1971)

    Article  MATH  Google Scholar 

16. Ogata, W., Kurosawa, K., Stinson, D.R., Saido, H.: New combinatorial designs and their applications to authentication codes and secret sharing schemes. Discrete Math. 279, 383–405 (2004)

    Article  MathSciNet  MATH  Google Scholar 

17. Morgan, J.P.: Nested designs. In: Colbourn, C.J., Dinitz, J.H. (eds.) The CRC Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton, pp. 535–540 (2007)

18. Raghavarao, D.: Constructions and Combinatorial Problems in Design of Experiments. Dover, New York (1988)

    MATH  Google Scholar 

19. Sawa, M.: On a symmetric representation of Hermitian matrices and its applications to graph theory. J. Combin. Theory Ser. B. 116, 484–503 (2016)

    Article  MathSciNet  MATH  Google Scholar 

20. Wang, J., Su, R.: Further results on the existence of splitting BIBDs and application to authentication codes. Acta Appl. Math. 109, 791–803 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references