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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.

has been cited by the following article:

• TITLE: Partition and the Perfect Codes in the Additive Channel

  AUTHORS: Garib Movsisyan

  KEYWORDS: Partition; Perfect Codes; Additive Channel

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.3 No.3, July 2, 2013

  ABSTRACT: Many problems of discrete optimization are connected with partition of the n-dimensional space into certain subsets, and the requirements needed for these subsets can be geometrical—for instance, their sphericity—or they can be connected withcertain metrics—for instance, the requirement that subsets are Dirichlet’s regions with Hamming’s metrics [1]. Often partitions into some subsets are considered, on which a functional is optimized [2]. In the present work, the partitions of the n-dimensional space into subsets with “zero” limitation are considered. Such partitions allow us to construct the set of the group codes, V, and the set of the channels, A, between the arbitrary elements, V and A, having correcting relation between them. Descriptions of some classes of both perfect and imperfect codes in the additive channel are presented, too. A way of constructing of group codes correcting the errors in the additive channels is presented, and this method is a further generalization of Hamming’s method of code construction.