A new proof to complexity of dual basis of a type I optimal normal basis

Baofeng Wu; Kai Zhou; Zhuojun Liu

A new proof to complexity of dual basis of a type I optimal normal basis

Discrete Mathematics 2013-01-03 v3 Combinatorics

Authors: Baofeng Wu , Kai Zhou , Zhuojun Liu

Abstract

The complexity of dual basis of a type I optimal normal basis of $\mathbb{F}_{q^n}$ over $\mathbb{F}_{q}$ was determined to be $3n-3$ or $3n-2$ according as $q$ is even or odd, respectively, by Z.-X. Wan and K. 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.

Keywords

dual basis optimal normal basis complexity finite fields polynomial basis Galois fields algebraic complexity

Cite

@article{arxiv.1112.3153,
  title  = {A new proof to complexity of dual basis of a type I optimal normal basis},
  author = {Baofeng Wu and Kai Zhou and Zhuojun Liu},
  journal= {arXiv preprint arXiv:1112.3153},
  year   = {2013}
}

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7 pages

A new proof to complexity of dual basis of a type I optimal normal basis

Abstract

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