A relation between self-re ciprocal transformation and normal basis over odd characteristic field

Shigeki Kobayashi, Yasuyuki Nogami, Tatsuo Sugimura

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let q and f (x) be an odd characteristic and an irreducible polynomial of degree m over Fq , respectively. Then, suppose that F(x) = x m f (x + x-1) becomes irreducible over Fq . This paper shows that the conjugate zeros of F(x) with respect to Fq form a normal basis in Fq2m if and only if those of f (x) form a normal basis in Fqm and the part of conjugates given as follows are linearly independent over Fq , {γ - γ-1, (γ - γ-1)q, ⋯ , (γ - γ-1) qm-1 }, where γ is a zero of F(x) and thus a proper element in Fq2m . In addition, from the viewpoint of q-polynomial, this paper proposes an efficient method for checking whether or not the conjugate zeros of F(x) satisfy the condition.

Original languageEnglish
Pages (from-to)1923-1931
Number of pages9
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE93-A
Issue number11
DOIs
Publication statusPublished - Nov 2010

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Normal Basis
Odd
Polynomials
Zero
Irreducible polynomial
Linearly
If and only if
Polynomial

Keywords

  • Normal basis
  • Self-reciprocal irreducible polynomial

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics
  • Signal Processing

Cite this

A relation between self-re ciprocal transformation and normal basis over odd characteristic field. / Kobayashi, Shigeki; Nogami, Yasuyuki; Sugimura, Tatsuo.

In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E93-A, No. 11, 11.2010, p. 1923-1931.

Research output: Contribution to journalArticle

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