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A new proof to the complexity of the dual basis of a type-Ⅰ optimal normal basis over finite fields
Received date: 2013-03-04
Revised date: 2013-09-06
Online published: 2014-09-15
Supported by
Supported by National Basic Research Program of China (2011CB302400) and National Natural Science Foundation of China(11301509)
The complexity of the dual basis of a type-Ⅰ optimal normal basis of Fqn over Fq was determined to be 3n-3 or 3n-2 according as q is even or odd, respectively, by Wan and Zhou in 2007. We give a new proof to this result by clearly deriving the dual of a type-Ⅰ optimal normal basis with the aid of a lemma on the dual of a polynomial basis.
Key words： optimal normal basis; dual basis; complexity; polynomial basis
WU Baofeng , ZHOU Kai , LIU Zhuojun . A new proof to the complexity of the dual basis of a type-Ⅰ optimal normal basis over finite fields[J]. Journal of University of Chinese Academy of Sciences, 2014 , 31(5) : 586 -589 . DOI: 10.7523/j.issn.2095-6134.2014.05.002
[1] Lidl R, Niederreiter H. finite fields[M]. 2nd ed. Cambridge: Cambridge University Press, 1997.
[2] Mullin R, Onyszchuk I, Vanstone S, et al. Optimal normal bases in GF(pn)[J]. Discrete Appl Math, 1988/1989, 22:149-161.
[3] Menezes A, Blake I, Gao X, et al. Applications of finite fields[M]. Boston: Kluwer Academic, 1993.
[4] Liao Q Y, Sun Q. On multiplication tables of optimal normal bases over finite fields[J]. Acta Math Sin: Chinese Ser, 2005, 48(5):947-954.
[5] Wan Z X, Zhou K. On the complexity of the dual basis of a type I optimal normal basis[J]. Finite Fields Appl, 2007, 13(1):411-417.
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