### Abstract

This paper proposes a useful method for constructing a self-dual normal basis in an arbitrary extension field F_{pm} such that 4p does not divide m (p - 1) and m is odd. In detail, when the characteristic p and extension degree m satisfies the following conditions (1) and either (2a) or (2b); (1) 2 k m + 1 is a prime number, (2a) the order of p in F_{2 k m + 1} is 2 k m, (2b) 2 {does not divide} k m and the order of p in F_{2 k m + 1} is km, we can consider a class of Gauss period normal bases. Using this Gauss period normal basis, this paper shows a method to construct a self-dual normal basis in the extension field F_{pm}.

Original language | English |
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Pages (from-to) | 867-876 |

Number of pages | 10 |

Journal | Finite Fields and their Applications |

Volume | 14 |

Issue number | 4 |

DOIs | |

Publication status | Published - Nov 1 2008 |

### Keywords

- Extension field
- Gauss period normal basis
- Self-dual normal basis

### ASJC Scopus subject areas

- Theoretical Computer Science
- Algebra and Number Theory
- Engineering(all)
- Applied Mathematics

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## Cite this

Nogami, Y., Nasu, H., Morikawa, Y., & Uehara, S. (2008). A method for constructing a self-dual normal basis in odd characteristic extension fields.

*Finite Fields and their Applications*,*14*(4), 867-876. https://doi.org/10.1016/j.ffa.2008.04.001