20
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Recursive construction of normal polynomials over finite fields

, &
Pages 2645-2660 | Received 01 Oct 2020, Published online: 03 Aug 2021

References

  • Abdullah, A., Gajera, H. and Mahalanobis, A. (2016). On improvements of the r-adding walk in a finite field of characteristic 2, Journal of Discrete Mathematical Sciences and Cryptography, 19:1, 13-38. doi: 10.1080/09720529.2015.1084782
  • Abrahamyan, S., Alizadeh, M. and Kyuregyan, M. K. (2012). Recursive constructions of irreducible polynomials over finite fields, Finite Fields and its Applications, 18, 738-745. doi: 10.1016/j.ffa.2012.03.003
  • Abrahamyan, S. and Kyuregyan, M. K. (2011). A recurrent method for constructing irreducible polynomials over finite fields, Computer algebra in Scientific Computing, eds. Gerdt, V. P., Koepf, W., Mayr, E.W. and Vorozhtsov, E. V., LNCS, Vol. 6885, 1-9.
  • Alizadeh, M. and Mehrabi, S. (2015). Construction of self-reciprocal normal polynomials over finite fields of even characteristic, Turkish Journal of Mathematics, 39, 259-267. doi: 10.3906/mat-1407-32
  • Alizadeh, M., Darafsheh, M. R. and Mehrabi, S. (2018). On the k-normal elements and polynomials over finite fields, Italian Journal of Pure and Applied Mathematics, 39, 451-464.
  • Baumbaugh, T. and Manganiello, F. (2019). Matroidal root structure of skew polynomials over finite fields, Journal of Discrete Mathematical Sciences and Cryptography, 22:3, 377-389. doi: 10.1080/09720529.2019.1600845
  • Cohen, S. D. (1969). On irreducible polynomials of certain types in finite fields, Math. Proc. Cambridge Philos. Soc., 66, 335-344. doi: 10.1017/S0305004100045023
  • Gao, S. (1993). Normal bases over finite fields, Ph. D. Thesis, University of Waterloo, Waterloo, Canada.
  • Kim, R. and Son, H. S. (2020). Recursive constructions of k-normal polynomials using some rational transformations over finite fields, Journal of Algebra and its Applications, 2050210, 1-16.
  • Kyuregyan, M. K. (2002). Recurrent methods for constructing irreducible polynomials over GF(2s), Finite Fields and its Applications, 8, 52-68. doi: 10.1006/ffta.2001.0323
  • Kyuregyan, M. K. (2004). Iterated constructions of irreducible polynomials over finite fields with linearly independent roots, Finite Fields and its Applications, 10, 323-341. doi: 10.1016/j.ffa.2003.09.002
  • Kyuregyan, M. K. (2008). Recursive constructions of N-Polynomials over GF(2s), Discrete Applied Mathematics, 156, 1554-1559. doi: 10.1016/j.dam.2006.11.014
  • Lidl, R. and Niederreiter, H. (1983). Finite Fields, Encyclopedia of Mathematics and its Applications, Addison-Wesley, Reading, MA, Vol. 20.
  • Menezes, A. J., Blake, I. F., Gao, X., Mullin, R. C., Vanstone, S. A. and Yaghoobian, T. (1993). Applications of Finite Fields, Kluwer Academic Publishers, Boston, Dordrecht, Lancaster.
  • Meyn, H. (1995). Explicit N-Polynomials of 2-power degree over finite fields, Designs, Codes and Cryptography, 6, 107-116. doi: 10.1007/BF01398009
  • Scheerhorn, A. (1994). Iterated constructions of normal bases over finite fields, In: Mullen, G. L. and Shiue, P. J. S., editors, Finite Fields: Theory, Applications and Algorithms, Contemporary Mathematics, American Mathematical Society, Providence, RI.
  • Schwartz, S. (1988). Irreducible polynomials over finite fields with linearly independent roots, Math. Slovaca, 38, 147-158.
  • Varshamov, R. R. (1984). A general method of synthesizing irreducible polynomials over Galois Fields, Soviet Math. Dokl, 29, 334-336.
  • Yi, H., Nie, Z. and Li, B. (2018). Efficient implementations of Gaussian elimination in finite fields on ASICs for MQ cryptographic systems, Journal of Discrete Mathematical Sciences and Cryptography, 21:3, 797-802. doi: 10.1080/09720529.2018.1449354

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.