Skip to main content
SpringerLink
Log in

On the Number of Two-Weight Cyclic Codes with Composite Parity-Check Polynomials

  • Conference paper
Arithmetic of Finite Fields (WAIFI 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5130))

Included in the following conference series:

  • 647 Accesses

Abstract

Sufficient conditions for the construction of a two-weight cyclic code by means of the direct sum of two one-weight cyclic codes, were recently presented in [4]. On the other hand, an explicit formula for the number of one-weight cyclic codes, when the length and dimension are given, was proved in [3]. By imposing some conditions on the finite field, we now combine both results in order to give a lower bound for the number of two-weight cyclic codes with composite parity-check polynomials.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Lidl, R., Niederreiter, H.: Finite Fields. Cambridge Univ. Press, Cambridge (1983)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  3. Vega, G.: Determining the Number of One-weight Cyclic Codes when Length and Dimension are Given. In: Carlet, C., Sunar, B. (eds.) WAIFI 2007. LNCS, vol. 4547, pp. 284–293. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Vega, G.: Two-weight cyclic codes constructed as the direct sum of two one-weight cyclic codes, Finite Fields Appl. (in press, 2008), doi:10.1016/j.ffa.2008.01.002

    Google Scholar 

  5. Wolfmann, J.: Are 2-Weight Projective Cyclic Codes Irreducible? IEEE Trans. Inform. Theory. 51, 733–737 (2005)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dirección General de Servicios de Cómputo Académico, Universidad Nacional Autónoma de México, 04510, México D.F., Mexico

    Gerardo Vega

Authors
  1. Gerardo Vega
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Joachim von zur Gathen José Luis Imaña Çetin Kaya Koç

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vega, G. (2008). On the Number of Two-Weight Cyclic Codes with Composite Parity-Check Polynomials. In: von zur Gathen, J., Imaña, J.L., Koç, Ç.K. (eds) Arithmetic of Finite Fields. WAIFI 2008. Lecture Notes in Computer Science, vol 5130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69499-1_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-69499-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69498-4

  • Online ISBN: 978-3-540-69499-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation