Skip to main content
SpringerLink
Log in

A note about the cyclotomic polynomial Φ pq (x) and some related results

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

The expression of cyclotomic polynomial Φ pq (x) is concerned for a long time. A simple and explicit expression of Φ pq (x) in Z[x] has been showed. The form of the factors of Φ pq (x) over F 2 and the upper, lower bounds of their Hamming weight are provided.

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. Migotti A. Zur Theorie der Kreisteilungsgleichung, S.-B der Math.-Naturwiss. Class der Kaiserlichen Akademie der Wissenschaften, Wien, 1883, 87: 7–14.

    Google Scholar 

  2. Beiter M. The midterm coefficient of the cyclotomic polynomial Φpq(x), Amer Math Monthly, 1964, 71: 769–770.

    Article  MATH  MathSciNet  Google Scholar 

  3. Carlitz L. The number of terms in the cyclotomic polynomial Φpq(x), Amer Math Monthly, 1966, 73: 979–981.

    Article  MATH  MathSciNet  Google Scholar 

  4. Lam T Y, Leung K H. On the cyclotomic polynomial Φpq(x), Amer Math Monthly, 1996, 103: 562–564.

    Article  MATH  MathSciNet  Google Scholar 

  5. Lidl R, Niederreiter H. Finite Fields, Encyclopaedia of Mathematics and Its Applications, vol 20 Reading, MA: Addision Wesley, 1983.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Appl. Math., Zhengzhou Inform. Eng. Univ., Zhengzhou, 450002, China

    Feng-xiang Zhu & Wen-feng Qi

Authors
  1. Feng-xiang Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wen-feng Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the National Natural Science Foundation of China (60673081) and the National 863 Plan(2006AA01Z417).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, Fx., Qi, Wf. A note about the cyclotomic polynomial Φ pq (x) and some related results. Appl. Math. J. Chin. Univ. 23, 245–250 (2008). https://doi.org/10.1007/s11766-008-0216-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-008-0216-y

MR Subject Classification

Keywords

Search

Navigation