Construction of Irreducible Polynomials over F5 and F7

Authors

  • Neetu Dhiman University Institute of Technology, Himachal Pradesh University, Shimla, H. P.
  • Balkaran Singh Himachal Pradesh University, Shimla, 171005, Himachal Pradesh, India
  • Praveen Agarwal Anand International College of Engineering, Jaipur, 303012, Rajasthan, India
  • Shabnam Sharma 4PVCNSSK Govt. Polytechnic College Bilaspur, 174035, Himachal Pradesh, India

DOI:

https://doi.org/10.5269/bspm.76034

Abstract

Construction of irreducible polynomials is crucial because of their implications in formulating
error correcting codes, linear feedback shift register designs and to study algebraic complexity
of polynomials. Irreducible polynomials also help us to generate non-zero elements of Finite
Fields. In this manuscript, we construct and characterize the structure of F∗5n and F∗7n in terms
of conjugate elements. Further, a technique to generate degree n irreducible polynomials over
F5 and F7 is also developed.

Author Biographies

  • Balkaran Singh, Himachal Pradesh University, Shimla, 171005, Himachal Pradesh, India

    Department of Mathematics and Statistics

  • Praveen Agarwal, Anand International College of Engineering, Jaipur, 303012, Rajasthan, India

    Department of Mathematics

  • Shabnam Sharma, 4PVCNSSK Govt. Polytechnic College Bilaspur, 174035, Himachal Pradesh, India

    Department of  Applied Sciences & Humanities

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Published

2025-09-30

Issue

Vol. 43 (2025)

Section

Research Articles

License

When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).

The journal utilize the Creative Common Attribution (CC-BY 4.0).

 

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