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Problemy Peredachi Informatsii, 2003, Volume 39, Issue 2, Pages 23–28
(Mi ppi214)
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This article is cited in 12 scientific papers (total in 12 papers)
Information Theory and Coding Theory
To Metric Rigidity of Binary Codes
S. V. Avgustinovich, F. I. Solov'eva
Abstract:
A code $C$ in the $n$-dimensional metric space $E^n$ over $GF(2)$ is called metrically rigid if each isometry $I\colon C\to E^n$ can be extended to an isometry of the whole space $E^n$. For $n$ large enough, metrical rigidity of any length-$n$ binary code that contains a $2-(n,k,\lambda)$–design is proved. The class of such codes includes, for instance, all families of uniformly packed codes of large enough lengths that satisfy the condition $d-\rho\geq 2$, where $d$ is the code distance and $\rho$ is the covering radius.
Received: 14.06.2002 Revised: 04.09.2002
Citation:
S. V. Avgustinovich, F. I. Solov'eva, “To Metric Rigidity of Binary Codes”, Probl. Peredachi Inf., 39:2 (2003), 23–28; Problems Inform. Transmission, 39:2 (2003), 178–183
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https://www.mathnet.ru/eng/ppi214 https://www.mathnet.ru/eng/ppi/v39/i2/p23
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Abstract page: | 482 | Full-text PDF : | 125 | References: | 40 | First page: | 2 |
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