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On LDPC codes corresponding to affine parts of generalized polygons

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Języki publikacji
EN
Abstrakty
EN
In this paper we describe how to use special induced subgraphs of generalized m-gons to obtain the LDPC error correcting codes. We compare the properties of codes related to the affine parts of q-regular generalised 6-gons with the properties of known LDPC codes corresponding to the graphs D(5, q).
Słowa kluczowe
Rocznik
Strony
143--152
Opis fizyczny
Bibliogr. 18 poz., rys.
Twórcy
autor
  • Institute of Mathematics, Maria Curie-Sklodowska University, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland
autor
  • Institute of Mathematics, Maria Curie-Sklodowska University, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland
Bibliografia
  • [1] Ustimenko V., Woldar A., Extremal properties of regular and affine generalized polygons as tactical configurations, European Journal of Combinatorics 24 (2003):99.
  • [2] Guinand P., Lodge J., Tanner type codes arising from large girth graphs, Canadian Workshop on Information Theory CWIT ’97, Toronto, Ontario, Canada (June 3-6 1997): 5.
  • [3] Guinand P., Lodge J., Graph theoretic construction of generalized product codes, IEEE International Symposium on Information Theory ISIT’97 Ulm, Germany (June 29-July 4 1997):111.
  • [4] Lazebnik F., Ustimenko V. A., New examples of graphs without small cycles and of large size, European Journal of Combinatorics 14 (1993): 445.
  • [5] Lazebnik F., Ustimenko V. A., Woldar A. J., A characterization of the components of the graphs D(k; q), Discrete Mathematics 157 (1996): 271.
  • [6] Lazebnik F., Ustimenko V., Explicit construction of graphs with an arbitrary large girth and of large size, Discrete Applied Mathematics 60 (1995): 275.
  • [7] Lazebnik F., Ustimenko V. A., Woldar A. J., A new series of dense graphs of high girth, Bulletin (New Series) of the AMS, 32(1) (1995): 73.
  • [8] Tanner R. M., A recursive approach to low density codes, IEEE Transactions on Information Theory IT 27(5) (1984): 533.
  • [9] Gallager R. G., Low-Density Parity-Checks Codes, IRE Trans of Info Thy 8 (1962): 21.
  • [10] Huffman W. C., Pless V., Fundamentals of error correcting codes, first edition, Cambridge University Press, Cambridge, 2003.
  • [11] Shannon C. E., A Mathematical Theory of Communication, Bell System Technical Journal 27 (1948): 379.
  • [12] Shannon C. E., Weaver Warren, The Mathematical Theory of Communication, Univ Of Illinois Pr 1963.
  • [13] Brower A.,Cohen A., Nuemaier A., Distance regular graphs, Springer, Berlin, 1989.
  • [14] Bollobas B., Extremal Graph Theory. Academic Press, 1978.
  • [15] Shokrollahi A., LDPC Codes: An Introduction, Digital Fountain Inc, Fremont (2002), available from: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.110.1008.
  • [16] Shaska T., Ustimenko V., On some applications of graph theory to cryptography and turbocoding, Special issue of Albanian Journal of Mathematics:Proceedings of the NATO Advanced Studies Institute ”New challenges in digital communications”, May 2008, University of Vlora 2(3) (2008): 249.
  • [17] Ustimenko V. A., On the extremal regular directed graphs without commutative diagrams and their applications in coding theory and cryptography, Albanian. J. of Mathematics, Special Issue Algebra and Computational Algebraic Geometry 1(N4) (2007): 387.
  • [18] Shaska T., Huffman W. C., Joener D., Ustimenko V. (editors), Advances in Coding Theory and Cryptography, Series on Coding and Cryptology 3 (2007): 181.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a82e463d-5602-4f5c-8be1-556406c2212f
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