Research ArticleOpen AccessGoogle Scholar indexed
The Code of the Symmetric Net with m = 4 and μ = 2
- 1
Open Journal of Discrete Mathematics·Volume 02 (2012)·Pages 1–4·Published 20 January 2012·DOI10.4236/ojdm.2012.21001
Copy link · social · email
Abstract
In this paper, we investigated the code over GF(2) which is generated by the incidence matrix of the symmetric (2,4) - net D. By computer search, we found that this binary code of D has rank 13 and the minimum distance is 8.
KeywordsSymmetric NetsCodes
- T. Beth, D. Jungnickel and H. Lenz, “Design Theory,” Cambridge University Press, Cambridge, 1999.
- C. J. Colbourn and J. H. Dinitz, “The CRC Handbook of Combinatorial Designs,” CRC Press, Boca Raton, New York, London, Tokyo, 1996.
- Y. J. Ionin and M. S. Shrikhande, “Combinatorics of Symmetric Designs,” Cambridge University Press, Cambridge, 2006.
- A. N. Al-Kenani and V. C. Mavron, “Non-Tactical Symmetric Nets,” Journal of the London Mathematical Society, Vol. 67, No. 2, 2003, pp. 273-288. doi:10.1112/S0024610702004052
- V. C. Mavron and V. D. Tonchev, “On Symmetric Nets and Generalised Hadamard Matrices from Affine Designs,” Journal of Geometry, Vol. 67, No. 1-2, 2000, pp. 180-187. doi:10.1007/BF01220309
- A. T. Butson, “Generalized Hadamard Matrices,” Proceedings of the American Mathematical Society, Vol. 13, 1962, pp. 894-898. doi:10.1090/S0002-9939-1962-0142557-0
- D. Jungnickel, “On Difference Matrices, Resolvable Transversal Designs and Generalised Hadamard Matrices,” Mathematische Zeitschrift, Vol. 167, No. 1, 1979, pp. 49-60. doi:10.1007/BF01215243
- E. F. Assmus Jr. and J. D. Key, “Designs and Their Codes,” Cambridge Tracts in Mathematics, Vol. 103, Cambridge University Press, 1992.
- V. D. Tonchev, “Quasi-Symmetric Designs, Codes, Quadrics, and Hyperplane Sections,” Geometriae Dedicata, Vol. 48, No. 3, 1993, pp. 295-308. doi:10.1007/BF01264073