The Code of the Symmetric Net with m = 4 and μ = 2
Author(s)
Ahmad N. Al-Kenani
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.
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.
Cite this paper
A. Al-Kenani, "The Code of the Symmetric Net with m = 4 and μ = 2," Open Journal of Discrete Mathematics, Vol. 2 No. 1, 2012, pp. 1-4. doi: 10.4236/ojdm.2012.21001.
A. Al-Kenani, "The Code of the Symmetric Net with m = 4 and μ = 2," Open Journal of Discrete Mathematics, Vol. 2 No. 1, 2012, pp. 1-4. doi: 10.4236/ojdm.2012.21001.
References
[1] T. Beth, D. Jungnickel and H. Lenz, “Design Theory,” Cambridge University Press, Cambridge, 1999. [2] C. J. Colbourn and J. H. Dinitz, “The CRC Handbook of Combinatorial Designs,” CRC Press, Boca Raton, New York, London, Tokyo, 1996. [3] Y. J. Ionin and M. S. Shrikhande, “Combinatorics of Symmetric Designs,” Cambridge University Press, Cambridge, 2006. [4] 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 [5] 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 [6] 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 [7] 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 [8] E. F. Assmus Jr. and J. D. Key, “Designs and Their Codes,” Cambridge Tracts in Mathematics, Vol. 103, Cambridge University Press, 1992. [9] 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
[1] T. Beth, D. Jungnickel and H. Lenz, “Design Theory,” Cambridge University Press, Cambridge, 1999. [2] C. J. Colbourn and J. H. Dinitz, “The CRC Handbook of Combinatorial Designs,” CRC Press, Boca Raton, New York, London, Tokyo, 1996. [3] Y. J. Ionin and M. S. Shrikhande, “Combinatorics of Symmetric Designs,” Cambridge University Press, Cambridge, 2006. [4] 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 [5] 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 [6] 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 [7] 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 [8] E. F. Assmus Jr. and J. D. Key, “Designs and Their Codes,” Cambridge Tracts in Mathematics, Vol. 103, Cambridge University Press, 1992. [9] 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