### Abstract

Let q and f(x) be an odd characteristic and an irreducible polynomial of degree m over F_{q}, respectively. Then, suppose that F(x) = x ^{m} f(x+x^{-1}) is irreducible over F_{q}. This paper shows that the conjugate zeros of F(x) with respect to F_{q} form a normal basis in F_{q}2m if and only if those of f(x) form a normal basis in F_{q}m and the partial conjugates given as follows are linearly independent over F_{q}, {γ - γ^{-1}, (γ - γ^{-1})^{q}, · · · , (γ - γ^{-1})qm-1}, (1) where γ is a zero of F(x) and thus a proper element in F_{q}2m. 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 language | English |
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Title of host publication | ICCIT 2009 - 4th International Conference on Computer Sciences and Convergence Information Technology |

Pages | 999-1004 |

Number of pages | 6 |

DOIs | |

Publication status | Published - Dec 1 2009 |

Event | 4th International Conference on Computer Sciences and Convergence Information Technology, ICCIT 2009 - Seoul, Korea, Republic of Duration: Nov 24 2009 → Nov 26 2009 |

### Publication series

Name | ICCIT 2009 - 4th International Conference on Computer Sciences and Convergence Information Technology |
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### Other

Other | 4th International Conference on Computer Sciences and Convergence Information Technology, ICCIT 2009 |
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Country | Korea, Republic of |

City | Seoul |

Period | 11/24/09 → 11/26/09 |

### Keywords

- Normal basis
- Polynomial transformation
- Self-reciprocal irreducible polynomial

### ASJC Scopus subject areas

- Computer Science(all)
- Information Systems and Management

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## Cite this

*ICCIT 2009 - 4th International Conference on Computer Sciences and Convergence Information Technology*(pp. 999-1004). [5369570] (ICCIT 2009 - 4th International Conference on Computer Sciences and Convergence Information Technology). https://doi.org/10.1109/ICCIT.2009.119