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Rectangular Codes and Rectangular Algebra

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1719))

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Abstract

We investigate general properties of rectangular codes. The class of rectangular codes includes all linear, group, and many nongroup codes.We define a basis of a rectangular code. This basis gives a universal description of a rectangular code.

In this paper the rectangular algebra is defined.We show that all bases of a t-rectangular code have the same cardinality. Bounds on the cardinality of a basis of a rectangular code are given.

The work was supported by Russian Fundamental Research Foundation (project No 99-01-00840) and by Deutsche Forschungs Gemeinschaft (Germany).

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References

  1. F. R. Kschischang, “The trellis structure of maximal fixed-cost codes,” IEEE Trans. Inform. Theory, vol. 42, Part I, no. 6, pp. 1828–1838, Nov. 1996.

    Article  MATH  MathSciNet  Google Scholar 

  2. V. Sidorenko, “The Euler characteristic of the minimal code trellis is maximum,” Problems of Inform. Transm. vol. 33, no. 1, pp. 87–93, January-March. 1997.

    MathSciNet  Google Scholar 

  3. V. Sidorenko, I. Martin, and B. Honary “On the rectangularity of nonlinear block codes,” IEEE Trans. Inform. Theory, vol. 45, no. 2, pp. 720–725, March 1999.

    Article  MATH  MathSciNet  Google Scholar 

  4. Y. Shany and Y. Be’ery, “On the trellis complexity of the Preparata and Goethals codes,” to appear in IEEE Trans. Inform. Theory.

    Google Scholar 

  5. A. Vardy and F. R. Kschischang, “Proof of a conjecture of McEliece regarding the optimality of the minimal trellis,” IEEE Trans. Inform. Theory, vol. 42, Part I, no. 6, pp. 2027-1834, Nov. 1996.

    Article  MathSciNet  Google Scholar 

  6. R. Lucas, M. Bossert, M. Breitbach, “Iterative soft-decision decoding of linear binary block codes,” in proceedings of IEEE International Symposium on Information Theory and its Applications, pp.811–814, Victoria, Canada, 1996.

    Google Scholar 

  7. S. Lin, T. Kasami, T. Fujiwara, and M. Fossorier, “Trellises and trellis-based decoding algorithms for linear block codes,” Boston: Kluwer Academic, 1998.

    MATH  Google Scholar 

  8. V. Sidorenko, J. Maucher, and M. Bossert, “On the Theory of Rectangular Codes,” in Proc. of 6th Intern. Workshop on Algebraic and Combinatorial Coding theory, Pskov, Russia, pp.207–210, Sept. 1998.

    Google Scholar 

  9. P.M. Cohn, Universal algebra, Harper and Row, New York, N.Y., 1965.

    MATH  Google Scholar 

  10. Yu. Sidorenko, “How many words can be generated by a rectangular basis”, preprint (in Russian).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Information Transmission Problems, Russian Academy of Science, B. Karetnyi per. 19, 101447, Moscow GSP-4, Russia

    V. Sidorenko

  2. Dept. of Information Technology, University of Ulm, Albert-Einstein-Allee 43, 89081, Ulm, Germany

    J. Maucher & M. Bossert

Authors
  1. V. Sidorenko
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  2. J. Maucher
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  3. M. Bossert
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Hawaii, 2540 Dole St., # 483, Honolulu, HI, 96822, USA

    Marc Fossorier  & Shu Lin  & 

  2. Institute of Industrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo, 106, Japan

    Hideki Imai

  3. AAECC/IRIT, Université Paul Sabatier, 118, Route de Narbonne, F31067, Toulouse, Cedex, France

    Alain Poli

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© 1999 Springer-Verlag Berlin Heidelberg

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Sidorenko, V., Maucher, J., Bossert, M. (1999). Rectangular Codes and Rectangular Algebra. In: Fossorier, M., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1999. Lecture Notes in Computer Science, vol 1719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46796-3_25

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  • DOI: https://doi.org/10.1007/3-540-46796-3_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66723-0

  • Online ISBN: 978-3-540-46796-0

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