On the Classification of Splitting (v, u×c, λ) BIBDs

Zhelezova, Stela

doi:10.2478/cait-2018-0023

Abstract

The (v, u×c, λ)-splitting balanced incomplete block designs correspond to c-splitting authentication codes. We classify splitting balanced incomplete block designs with definite parameters.

References

1. Abel, R. J. R., G. Ge, J. Yin. Resolvable and Near-Resolvable Designs. – In: C. J. Colbourn, J. H. Dinitz, Eds. Handbook of Combinatorial Designs. 2nd Edition. Boca Raton, FL. CRC Press, 2007, pp. 124-132.
Search in Google Scholar Back to article
2. Bassalygo, L. A., V. A. Zinoviev. Remark on Balanced Incomplete Block Designs, Near-Resolvable Block Designs, and q-ary Constant-Weight Codes. – Problems of Information Transmissions, Vol. 53, 2017, No 3, pp. 51-54.10.1134/S0032946017010045
Search in Google Scholar Back to article
3. Bassalygo, L. A., V. S. Lebedev, V. A. Zinoviev. On m-Nearly Resolvable BIB Designs and q-ary Optimal Constant Weight Codes. – In: Proc. of 10th International Workshop on Coding and Cryptography, 18-22 September 2017, Saint-Petersburg, Russia.
Search in Google Scholar Back to article
4. Beth, T., D. Jungnickel, H. Lenz. Design Theory. Cambridge University Press, 1993.
Search in Google Scholar Back to article
5. C. J. Colbourn, J. H. Dinitz, Eds. Handbook of Combinatorial Designs. 2nd Edition – Discrete Mathematics and Its Applications, K. Rosen, Eds. Boca Raton, FL., CRC Press, 2007.
Search in Google Scholar Back to article
6. Du, B. Splitting Balanced Incomplete Block Designs with Block Size 3×2. – J. Combin. Des., Vol. 12, 2004, pp. 404-420.10.1002/jcd.20025
Search in Google Scholar Back to article
7. Du, B. Splitting Balanced Incomplete Block Designs. – Australas. J. Comb., Vol. 31, 2005, pp. 287-298.
Search in Google Scholar Back to article
8. Ge, G., Y. Miao, L. Wang. Combinatorial Constructions for Optimal Splitting Authentication Codes. – SIAM J. Discrete Math., Vol. 18, 2005, No 4, pp. 663-678.10.1137/S0895480103435469
Search in Google Scholar Back to article
9. Gilbert, E. N., F. J. MacWilliams, N. J. A. Sloane. Codes which Detect Deception. – Bell. System Tech. J., Vol. 53, 1974, pp. 405-424.10.1002/j.1538-7305.1974.tb02751.x
Search in Google Scholar Back to article
10. Haanpää, H., P. Kaski. The Near Resolvable 2-(13, 4, 3) Designs and Thirteen-Player Whist Tournaments. – Des. Codes Cryptogr., Vol. 35, 2005, No 3, pp. 271-285.10.1007/s10623-003-6738-7
Search in Google Scholar Back to article
11. Kaski, P., P. Östergård. Classification Algorithms for Codes and Designs. Berlin, Springer, 2006.
Search in Google Scholar Back to article
12. Morales, L. B., R. San Agustin,C. Velarde. Enumeration of All (2k + 1, k, k – 1)-NRBIBDs for 3 ≥ k ≥ 13, 2007. http://www.mcc.unam.mx/lbm/JCMCC05.pdf
Search in Google Scholar Back to article
13. Ogata, W., K. Kurosawa, D. R. Stinson, H. Saido. New Combinatorial Designs and Their Applications to Authentication Codes and Secret Sharing Schemes. – Discrete Math., Vol. 279, 2004, No 1-3, pp. 383-405.10.1016/S0012-365X(03)00283-8
Search in Google Scholar Back to article
14. Semakov, N., V. Zinoviev. Equidistant q-ary Codes with Maximal Distance and Resolvable Balanced Incomplete Block Designs. – Problems Inform. Transmission, Vol. 4, 1968, No 2, pp. 3-10.
Search in Google Scholar Back to article
15. Simmons, G. J. A Game Theory Model of Digital Message Authentication. – Congressus Numer., Vol. 34, 1982, pp. 413-424.
Search in Google Scholar Back to article
16. Su, R., J. Wang. On the Existence of (v, 3×3, λ)-Splitting Balanced Incomplete Block Design with λ between 2 to 9. – Journal of Shanghai Jiaotong University (Science), Vol. 3, 2008, No 4, pp. 482-486.10.1007/s12204-008-0482-0
Search in Google Scholar Back to article
17. Su, R., J. Wang. Further Results on the Existence of Splitting BIBDs and Application to Authentication Codes. – Acta Appl. Math., Vol. 109, 2010, No 3, pp. 791-803.10.1007/s10440-008-9346-8
Search in Google Scholar Back to article
18. Topalova, S., S. Zhelezova. Doubly Resolvable Designs with Small Parameters. – Ars Combin., Vol. 117, 2014, pp. 289-302.
Search in Google Scholar Back to article
19. Wang, J. A New Class of Optimal 3-Splitting Authentication Codes. – Des. Codes Cryptogr., Vol. 38, 2006, pp. 373-381.10.1007/s10623-005-1501-x
Search in Google Scholar Back to article

On the Classification of Splitting (v, u×c, λ) BIBDs

Abstract

Paradigm

My account