Skip to main content
SpringerLink
Log in
SpringerLink
Log in

On repeated-root cyclic codes and the two-way chain condition

  • Conference paper
  • First Online:
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1255))

Abstract

Some repeated-root cyclic codes are shown to satisfy the two-way chain condition. Necessary or sufficient conditions for codes satisfying the two-way chain condition are derived. Parameters of codes which do not admit efficient coordinate ordering are provided.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berger, Y., Be'ery, Y.: The twisted squaring construction, trellis complexity and generalized weights of BCH and QR codes. IEEE Trans. Inf. Theory 42 (1996) 1817–1827

    Google Scholar 

  2. Castagnoli, G., Massey, J.L., Schoeller, Ph., von Seemann, N.: On repeated-root cyclic codes. IEEE Trans. Inf. Theory 37 (1991) 337–342

    Google Scholar 

  3. Dodunekov, S., Encheva, S.: On the uniqueness of some subcodes of the binary extended Golay code. Problems of Inf. Transmission 29 (1993) 38–43

    Google Scholar 

  4. Dodunekov, S., Manev, K., Tonchev, V.: On the covering radius of the optimal binary [15, 6, 6] codes. Proc. Third Int. Workshop on Inf. Theory Convolutional Codes: multi-user communications Sochi (1987) 211–213

    Google Scholar 

  5. Encheva, S.: On binary linear codes which satisfy the two-way chain condition. IEEE Trans. Inf. Theory 42 (1996) 1038–1047

    Google Scholar 

  6. Forney, G.D. Jr.: Dimension/Length Profiles and Trellis Complexity of Linear Block codes. IEEE Trans. Inf. Theory 40 (1994) 1741–1752

    Google Scholar 

  7. Forney, G.D. Jr.: Dimension/Length Profiles and Trellis Complexity of Lattices. IEEE Trans. Inf. Theory 40 (1994) 1753–1772

    Google Scholar 

  8. Helleseth, T., Kløve, T., Ytrehus, Ø.: Generalized Hamming weights of linear codes. IEEE Trans. Inf. Theory 38 (1992) 1133–1140

    Google Scholar 

  9. Kapralov, S.: Enumeration of the binary linear [24, 7, 10] codes. Proc. Fifth Int. Workshop on Alg. and Comb. Theory Bulgaria, (1996) 151–156

    Google Scholar 

  10. Kasami, K., 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. Inf. Theory 39 (1993) 242–245

    Google Scholar 

  11. Kiely, A.B., Dolinar S.J. Jr., McEliece R.J., Ekroot L.L., and Lin, W.: Trellis decoding complexity of linear block codes. IEEE Trans. Inf. Theory 42, (1996) 1687–1697

    Google Scholar 

  12. Kløve, T.: On codes satisfying the double chain condition. Discr. Math. (to appear)

    Google Scholar 

  13. van Lint, J.H.: Repeated-root cyclic codes. IEEE Trans. Inf. Theory 37 (1991) 343–345

    Google Scholar 

  14. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting codes. North-Holland Amsterdam (1977)

    Google Scholar 

  15. Massey, J.L., Costello, D.J. Jr., Justesen, J.: Polynomial weights and code constructions. IEEE Trans. Inf. Theory 19 (1973) 101–110

    Google Scholar 

  16. Wei, V.K.: Generalized Hamming weights for linear codes. IEEE Trans. Inf. Theory 37 (1991) 1412–1418

    Google Scholar 

  17. Wei, V.K., Yang, K.: On the generalized Hamming weights of product codes. IEEE Trans. Inf. Theory 39 (1993) 1709–1713

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Stord/Haugesund College, Skåregt. 103, 5500, Haugesund, Norway

    Sylvia Encheva

Authors
  1. Sylvia Encheva
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Teo Mora Harold Mattson

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Encheva, S. (1997). On repeated-root cyclic codes and the two-way chain condition. In: Mora, T., Mattson, H. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1997. Lecture Notes in Computer Science, vol 1255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63163-1_7

Download citation

  • DOI: https://doi.org/10.1007/3-540-63163-1_7

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63163-7

  • Online ISBN: 978-3-540-69193-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation