### Abstract

Let p and m be an odd characteristic and extension degree, respectively. Then, let ! be a primitive element in F∗_{pm}, a geometric sequence S = Ls_{i}r, s_{i} =(Tr(ω^{i})/p) for i = 0, 1, 2,... has been proposed together with its some properties, where Tr (·) is the trace function over F_{p} and (a/p) is Legendre symbol for a in F_{p}. This paper shows an efficient method for generating the sequence when the base field F_{pm} is defined by an irreducible binomial over F_{p} with small odd characteristic p.

Original language | English |
---|---|

Title of host publication | Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 719-721 |

Number of pages | 3 |

ISBN (Print) | 9784885522925 |

Publication status | Published - Dec 8 2014 |

Event | 2014 International Symposium on Information Theory and Its Applications, ISITA 2014 - Melbourne, Australia Duration: Oct 26 2014 → Oct 29 2014 |

### Other

Other | 2014 International Symposium on Information Theory and Its Applications, ISITA 2014 |
---|---|

Country | Australia |

City | Melbourne |

Period | 10/26/14 → 10/29/14 |

### Keywords

- irreducible binomial
- Legendre symbol
- odd characteristic
- primitive element
- trace

### ASJC Scopus subject areas

- Computer Science Applications
- Information Systems

### Cite this

*Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014*(pp. 719-721). [6979938] Institute of Electrical and Electronics Engineers Inc..

**An efficient generation of geometric sequences defined with trace and legendre symbol.** / Nogami, Yasuyuki; Tada, Kazuki; Uehara, Satoshi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014.*, 6979938, Institute of Electrical and Electronics Engineers Inc., pp. 719-721, 2014 International Symposium on Information Theory and Its Applications, ISITA 2014, Melbourne, Australia, 10/26/14.

}

TY - GEN

T1 - An efficient generation of geometric sequences defined with trace and legendre symbol

AU - Nogami, Yasuyuki

AU - Tada, Kazuki

AU - Uehara, Satoshi

PY - 2014/12/8

Y1 - 2014/12/8

N2 - Let p and m be an odd characteristic and extension degree, respectively. Then, let ! be a primitive element in F∗pm, a geometric sequence S = Lsir, si =(Tr(ωi)/p) for i = 0, 1, 2,... has been proposed together with its some properties, where Tr (·) is the trace function over Fp and (a/p) is Legendre symbol for a in Fp. This paper shows an efficient method for generating the sequence when the base field Fpm is defined by an irreducible binomial over Fp with small odd characteristic p.

AB - Let p and m be an odd characteristic and extension degree, respectively. Then, let ! be a primitive element in F∗pm, a geometric sequence S = Lsir, si =(Tr(ωi)/p) for i = 0, 1, 2,... has been proposed together with its some properties, where Tr (·) is the trace function over Fp and (a/p) is Legendre symbol for a in Fp. This paper shows an efficient method for generating the sequence when the base field Fpm is defined by an irreducible binomial over Fp with small odd characteristic p.

KW - irreducible binomial

KW - Legendre symbol

KW - odd characteristic

KW - primitive element

KW - trace

UR - http://www.scopus.com/inward/record.url?scp=84920527989&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920527989&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9784885522925

SP - 719

EP - 721

BT - Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014

PB - Institute of Electrical and Electronics Engineers Inc.

ER -