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

  • Viktor A. Kopyttcev and Vladimir G. Mikhailov EMAIL logo
Published/Copyright: August 20, 2016
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Discrete Mathematics and Applications
From the journal Discrete Mathematics and Applications Volume 26 Issue 4

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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Received: 2015-3-11
Published Online: 2016-8-20
Published in Print: 2016-8-1

2016 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Research Article
  3. Characterization of almost perfect nonlinear functions in terms of subfunctions
  4. Research Article
  5. Estimates for distribution of the minimal distance of a random linear code
  6. Research Article
  7. The distributions of interrecord fillings
  8. Research Article
  9. Galois theory for clones and superclones
  10. Research Article
  11. Overgroups of order 2n additive regular groups of a residue ring and of a vector space
https://doi.org/10.1515/dma-2016-0018
Keywords for this article
minimum distance of a linear code; explicit estimates of distribution functions; asymptotic estimates of distribution functions

Articles in the same Issue

  1. Frontmatter
  2. Research Article
  3. Characterization of almost perfect nonlinear functions in terms of subfunctions
  4. Research Article
  5. Estimates for distribution of the minimal distance of a random linear code
  6. Research Article
  7. The distributions of interrecord fillings
  8. Research Article
  9. Galois theory for clones and superclones
  10. Research Article
  11. Overgroups of order 2n additive regular groups of a residue ring and of a vector space
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