A Relation between Self-Reciprocal Transformation and Normal Basis over Odd Characteristic Field

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概要

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• Let q and f(x) be an odd characteristic and an irreducible polynomial of degree m over Fq, respectively. Then, suppose that F(x) = xmf(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.

• （社）電子情報通信学会の論文
• 2010-11-01

著者

• SUGIMURA TATSUO

  Faculty of Engineering, Shinshu University

• Kobayashi Shigeki

  Graduate School Of Agricultural Science Kobe University

• Nogami Yasuyuki

  Graduate School Natural Science And Technology Okayama University

• Sugimura Tatsuo

  Faculty Of Engineering Shinshu University

• Kobayashi Shigeki

  Graduate School Of Science And Technology Shinshu University

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• A Relation between Self-Reciprocal Transformation and Normal Basis over Odd Characteristic Field

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