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This article is cited in 2 scientific papers (total in 2 papers)
Perfect binary codes of infinite length
S. A. Malyugin Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
Abstract:
A subset $C$ of infinite-dimensional binary cube is called a perfect binary code with distance 3 if all balls of radius 1 (in the Hamming metric) with centers in $C$ are pairwise disjoint and their union cover this binary cube. Similarly, we can define a perfect binary code in zero layer, consisting of all vectors of infinite-dimensional binary cube having finite supports. In this article we prove that the cardinality of all cosets of perfect binary codes in zero layer is the cardinality of the continuum. Moreover, the cardinality of all cosets of perfect binary codes in the whole binary cube is equal to the cardinality of the hypercontinuum. Bibliogr. 9.
Keywords:
perfect binary code, Hamming code, Vasil'ev code, component, continuum, hypercontinuum.
Received: 31.03.2016 Revised: 29.08.2016
Citation:
S. A. Malyugin, “Perfect binary codes of infinite length”, Diskretn. Anal. Issled. Oper., 24:2 (2017), 53–67; J. Appl. Industr. Math., 11:2 (2017), 227–235
Linking options:
https://www.mathnet.ru/eng/da869 https://www.mathnet.ru/eng/da/v24/i2/p53
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Abstract page: | 236 | Full-text PDF : | 134 | References: | 46 | First page: | 5 |
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