References
-
Ahmadi O., Shparlinski I. E., Voloch J. F. Multiplicative order of Gauss periods. Intern. J. Number Theory 2010, 6 (4), 877-882.
doi: 10.1142/S1793042110003290
-
Burkhart J. F. et al. Finite field elements of high order arising from modular curves. Des. Codes Cryptogr. 2009, 51 (3), 301-314.
doi: 10.1007/s10623-008-9262-y
-
Cheng Q. On the construction of finite field elements of large order. Finite Fields Appl. 2005, 11 (3), 358-366.
doi: 10.1016/j.ffa.2005.06.001
-
Crandall R., Pomerance C. Prime Numbers, A Computational Perspective. Springer-Verlag, New York, 2005.
-
Gao S. Elements of provable high orders in finite fields. Proc. Amer. Math. Soc. 1999, 127 (6), 1615-1623.
doi: 10.1090/S0002-9939-99-04795-4
-
Huang M.D., Narayanan A.K. Finding primitive elements in finite fields of small characteristic. arXiv 1304.1206 2013.
-
Ito H., Kajiwara T., Song H. A. A tower of Artin-Schreier extensions of finite fields and its applications. JP J. Algebra Number Theory Appl. 2011, 22 (2), 111-125.
-
Lidl R., Niederreiter H.. Finite Fields. Cambridge Univ. Press, Cambridge, 1997.
-
Mullen G.L., Panario D. Handbook of finite fields. CRC Press, Boca Raton, FL, 2013.
-
Mullen G.L., Shparlinski I. E. Open problems and conjectures in finite fields. In: Cohen S.D., Niederreiter H. (Eds.) Finite Fields and Applications, London Math. Soc. Lecture Note Ser., 233. Cambridge Univ. Press, Cambridge, 1996.
-
Popovych R. Elements of high order in finite fields of the form $F_{q} [x]/\Phi _{r} (x)$. Finite Fields Appl. 2012, 18 (4), 700-710.
doi: 10.1016/j.ffa.2012.01.003
-
Popovych R. Elements of high order in finite fields of the form $F_{q} [x]/(x^{m}-a)$. Finite Fields Appl. 2013, 19 (1), 86-92.
doi: 10.1016/j.ffa.2012.10.006
-
Voloch J.F. Elements of high order on finite fields from elliptic curves. Bull. Austral. Math. Soc. 2010, 81 (3), 425-429.
doi: 10.1017/S0004972709001075
-
Wiedemann D. An iterated quadratic extension of GF(2). Fibonacci Quart. 1988, 26 (4), 290-295.