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Diskretn. Anal. Issled. Oper., 2017, Volume 24, Number 2, Pages 53–67 (Mi da869)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00507


DOI: https://doi.org/10.17377/daio.2017.24.535

Full text: PDF file (325 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2017, 11:2, 227–235

UDC: 519.8
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

Citation in format AMSBIB
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\paper Perfect binary codes of infinite length
\jour Diskretn. Anal. Issled. Oper.
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\pages 53--67
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\jour J. Appl. Industr. Math.
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\pages 227--235
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