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Moments of the support weight distribution of linear codes

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Abstract

In this work, we give the expectation and the covariance formulas for the support weight distributions of linear codes.

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References

  1. Blinovsky V., Erez U., Litsyn S.: Weight distribution moments of random linear/coset codes. Des. Codes Cryptogr. 57, 127–138 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Britz T.: Higher support matroids. Discret. Math. 307, 2300–2308 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Gallager R.G.: Low Density Parity-Check Codes. MIT Press, Cambridge (1963)

    Google Scholar 

  4. Helleseth T., Kløve T., Mykkeltveit J.: The weight distribution of irreducible cyclic codes with block length n 1 ((q l − 1)/N). Discret. Math. 18, 179–211 (1977)

    Article  MATH  Google Scholar 

  5. Helleseth T., Kløve T., Ytrehus O.: Generalized Hamming weights of linear codes. IEEE Trans. Inform. Theory 38, 1133–1140 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  6. Helleseth T., Kløve T., Levenshtein V.I., Ytrehus O.: Bounds on the minimum support weights. IEEE Trans. Inform. Theory 41, 432–440 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kac V., Cheung P.: Quantum Calculus. Springer, Universitext (2001)

    Google Scholar 

  8. Kasami T., Takata T., Fujiwara T., Lin S.: On the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes. IEEE Trans. Inform. Theory 39, 242–245 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kløve T.: Support weight distribution of linear codes. Discret. Math. 106/107, 311–316 (1992)

    Article  Google Scholar 

  10. Klyachko A.A., Özen  I.: Correlations between the ranks of submatrices and weights of random codes. Finite Fields Appl. 15, 497–516 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Tsfasman M.A., Vladut S.G.: Algebraic Geometric Codes. Kluwer Academic Publishers, Dordrecht (1991)

    Book  MATH  Google Scholar 

  12. Tsfasman M.A., Vladut S.G.: Geometric approach to higher weights. IEEE Trans. Inform. Theory 41(6), 1564–1588 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  13. van Lint J.H., Wilson R.M.: A Course in Combinatorics, 2nd edn. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  14. Wei V.: Generalized Hamming weights for linear codes. IEEE Trans. Inform. Theory 37(5), 1412–1418 (1991)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Çankırı Karatekin Üniversitesi, Cankiri, Turkey

    İbrahim Özen

  2. Karabük Üniversitesi, Karbuk, Turkey

    Eda Tekin

Authors
  1. İbrahim Özen
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  2. Eda Tekin
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Correspondence to İbrahim Özen.

Additional information

Communicated by T. Helleseth.

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Özen, İ., Tekin, E. Moments of the support weight distribution of linear codes. Des. Codes Cryptogr. 67, 187–196 (2013). https://doi.org/10.1007/s10623-011-9597-7

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  • DOI: https://doi.org/10.1007/s10623-011-9597-7

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