Welcome to Journal of University of Chinese Academy of Sciences,Today is

›› 2014, Vol. 31 ›› Issue (5): 586-589.DOI: 10.7523/j.issn.2095-6134.2014.05.002

Previous Articles     Next Articles

A new proof to the complexity of the dual basis of a type-Ⅰ optimal normal basis over finite fields

WU Baofeng, ZHOU Kai, LIU Zhuojun   

  1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2013-03-04 Revised:2013-09-06 Online:2014-09-15
  • Supported by:

    Supported by National Basic Research Program of China (2011CB302400) and National Natural Science Foundation of China(11301509)

Abstract:

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

CLC Number: