Skip to main content
SpringerLink
Log in

A property of the relative subcodes

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

The relative subcodes are closely related to the concept of the relative generalized Hamming weight. Using projective geometry methods and the concept of the relative generalized Hamming weight, the authors prove a property of the relative subcodes which substantially improves the existing result.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Y. Luo, C. Mitrpant, A. J. Han Vinck, and K. F. Chen, Some new characters on the wire-tap channel of type II, IEEE Trans. Inform. Theory, 2005, 51(3): 1222–1229.

    Article  MathSciNet  Google Scholar 

  2. L. H. Ozarow and A. D. Wyner, Wire-tap channel II, AT&T Bell Laboratories Technical Journal, 1984, 63(10): 2135–2157.

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. W. D. Chen and T. Kløve, The weight hierarchies of q-ary codes of dimension 4, IEEE Trans. Inform. Theory, 1996, 42(6): 2265–2272.

    Article  MATH  MathSciNet  Google Scholar 

  6. Z. H. Liu, W. D. Chen, and Y. Luo, The relative generalized Hamming weight of linear q-ary codes and their subcodes, Des. Codes Cryptogr., 2008, 48(2): 111–123.

    Article  MATH  MathSciNet  Google Scholar 

  7. Z. H. Liu and W. D. Chen, Notes on the value function, Des. Codes Cryptogr., 2010, 54(1): 11–19.

    Article  MATH  MathSciNet  Google Scholar 

  8. C. K. Ngai, R. W. Yeung, and Z. Zhang, Network generalized hamming weight, in NetCod’09, Lausanne, Switzerland, 2009: 48–53.

  9. Z. Zhang, Wiretap networks II with partial information leakage, in China COM’09, Xi’an, China, 2009: 1–5.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, China

    Zihui Liu

  2. Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100190, China

    Wende Chen

Authors
  1. Zihui Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wende Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zihui Liu.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant Nos. 60972033 and 60832001.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Z., Chen, W. A property of the relative subcodes. J Syst Sci Complex 23, 1231–1238 (2010). https://doi.org/10.1007/s11424-010-9249-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-010-9249-4

Key words

Search

Navigation