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).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
Y. Shany and Y. Be’ery, “On the trellis complexity of the Preparata and Goethals codes,” to appear in IEEE Trans. Inform. Theory.
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.
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.
S. Lin, T. Kasami, T. Fujiwara, and M. Fossorier, “Trellises and trellis-based decoding algorithms for linear block codes,” Boston: Kluwer Academic, 1998.
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.
P.M. Cohn, Universal algebra, Harper and Row, New York, N.Y., 1965.
Yu. Sidorenko, “How many words can be generated by a rectangular basis”, preprint (in Russian).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-46796-3_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66723-0
Online ISBN: 978-3-540-46796-0
eBook Packages: Springer Book Archive