OJDM  Vol.3 No.3 , July 2013
Dirichlet Regions and Perfect Codes in Additive Channel
Author(s) Garib Movsisyan*
ABSTRACT

In the present work, the class of metrics connected with subsets of the linear space on the field, GF(2), is considered and a number of facts are established, which allow us to express the correcting capacity of codes for the additive channel in terms of this metrics. It is also considered a partition of the metric space, Bn, by means of D-representable codes. The equivalence of D-representable and the perfect codes in the additive channel is proved.


Cite this paper
G. Movsisyan, "Dirichlet Regions and Perfect Codes in Additive Channel," Open Journal of Discrete Mathematics, Vol. 3 No. 3, 2013, pp. 137-142. doi: 10.4236/ojdm.2013.33025.
References
[1]   V. K. Leontyev and G. L. Movsisyan, “On the Additive Channel of Communication,” Reports of Academy of Sciences of Armenia, Vol. 104, No. 1, 2004, pp. 23-27.

[2]   V. K. Leontyev, G. L. Movsisyan and J. G. Margaryan, “Perfect Codes in Additive Channels,” Reports of RAS, Vol. 411, No. 3, 2006, pp. 306-309.

[3]   V. K. Leontyev, G. L. Movsisyan and J. G. Margaryan, “On Perfect Codes in Additive Channels,” Problems of Information Communication, Vol. 44, No. 4, 2008, pp. 12-19.

[4]   V. K. Leontyev, G. L. Movsisyan and J. G. Margaryan, “Codes in Additive Channels,” Report of the Academy of Sciences of Armenia, Vol. 110, No. 4, 2010, pp. 334-339.

[5]   F. J. M. Williams and N. J. A. Sloane, “The Theory of Error-Correcting Codes,” Bell Laboratories, Marray Hill, 1977.

[6]   V. K. Leontyev, G. L. Movsisyan and J. G. Margaryan, “Correction of Errors in the Additive Channel,” Vestnik RAU, Vol. 2, No. 1, 2010, pp. 12-25.

[7]   Yu. M. Movsisyan, “Higher Algebra and Number Theory,” Yerevan State University, Yerevan, 2008, p. 455.

[8]   V. K. Leontyev, G. L. Movsisyan and J. G. Margaryan, “Partition of N-Dimensional Space on GF(2) into Dirichlet’s Regions,” Vestnik RAU, Vol. 2, No. 1, 2011, pp. 26-41.

 
 
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