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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei


CiteScore 2018: 0.44

SCImago Journal Rank (SJR) 2018: 0.325
Source Normalized Impact per Paper (SNIP) 2018: 0.987

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1569-3929
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Volume 26, Issue 4

Issues

Estimates for distribution of the minimal distance of a random linear code

Viktor A. Kopyttcev / Vladimir G. Mikhailov
Published Online: 2016-08-20 | DOI: https://doi.org/10.1515/dma-2016-0018

Abstract

The distribution function of the minimum distance (the minimum weight of nonzero codewords) of a random linear code over a finite field is studied. Expicit bounds in the form of inequalities and asymptotic estimates for this distribution function are obtained.

Keywords: minimum distance of a linear code; explicit estimates of distribution functions; asymptotic estimates of distribution functions

Originally published in Diskretnaya Matematika (2015) 27, №2, 22-44 (in Russian).

References

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    Kopyttcev V. A., Mikhailov V. G., “Explicit estimates of the accuracy for the Poisson approximation to the distribution of the number of solutions of random inclusions”,Matematicheskie Voprosy Kriptografii, 6 :1 (2015), 57–79 (in Russian).Google Scholar

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    Zubkov A. M., Kruglov V. I., “Statistical characteristics of weight spectra of random linear codes over GF(p)”,Matematicheskie Voprosy Kriptografii, 5 :1 (2014), 27–38 (in Russian).Google Scholar

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About the article

Received: 2015-03-11

Published Online: 2016-08-20

Published in Print: 2016-08-01


Citation Information: Discrete Mathematics and Applications, Volume 26, Issue 4, Pages 203–211, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265, DOI: https://doi.org/10.1515/dma-2016-0018.

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2016 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

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