METHOD FOR FINDING THE ROOT OF A POLYNOMIAL OVER THE EXTENDED GALOIS FIELD ON BASIS OF ROOTS OF AFINE POLYNOMIAL

  • Khac Hoan Pham Le Quy Don Technical University
  • Tien Thai Nguyen Le Quy Don Technical University
  • Son Ha Vu Institute of Science and Technology
Keywords: Galois field, error control coding, polynomial basis, normal basis.

Abstract

The article proposes a method for finding the roots of a polynomial over an extended Galois field based on
the roots of an affine polynomial. The proposed method makes it possible to reduce the calculation delay in
comparison with traditional methods, which makes it possible to use in a high-speed communication system

Author Biographies

Khac Hoan Pham, Le Quy Don Technical University

Assoc. Prof., PhD

Tien Thai Nguyen, Le Quy Don Technical University

PhD

Son Ha Vu, Institute of Science and Technology

PhD

References

1. Bijan Ansari, Finite field arithmetic and its application in cryptography / Dissertation for the degree Doctor of Philosophy in Electrical Engineering, University of California, Los Angeles, 2012.
2. Elwyn R Berlekamp, Algebraic Coding Theory (Revised Edition), World Scientific Publishing Co. Pte. Ltd., 2015.
3. Mutter, V.M. Osnovy pomehoustojchivoj teleperedachi informacii, L.: Jenergoatomizdat, Leningradskoe otdelenie, 1990.
4. Konopel'ko, V.K. i dr. Teorija prikladnogo kodirovanija. Mn.: BGUIR, 2004.
5. F. J. MacWilliams, N. J. A.Sloane, The theory of error correction codes, Elselvier, 1977.
6. Fedorenko S. V., Trifonov P. V. Finding roots of polynomials over finite fields, IEEE Transactions on Communications, 2002, Vol. 50, Issue 11, pp. 1709– 1711
7. Johann Groβschadl, A low-power bit serial multiplier for finite fields GF(2m). 34th IEEE International symposium on ciruits and system, vol. IV, 2001.
8. Chin-Chin Chen, Chiou Yng Lee, Erl-Huei Lu, Scalable and systolic montgomery multipliers over GF(2m), IEICE Transaction Fundamentals, Vol. E91, No.7 July 2008.
Published
2022-08-22
How to Cite
Pham, Khac Hoan, Tien Thai Nguyen, and Son Ha Vu. 2022. “METHOD FOR FINDING THE ROOT OF A POLYNOMIAL OVER THE EXTENDED GALOIS FIELD ON BASIS OF ROOTS OF AFINE POLYNOMIAL”. EurasianUnionScientists, August, 21-28. https://fizmat-tech.euroasia-science.ru/index.php/Euroasia/article/view/827.