### 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 |
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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 (Electronic) | 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 |

### Publication series

Name | Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014 |
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### Other

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

City | Melbourne |

Period | 10/26/14 → 10/29/14 |

### Keywords

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

### ASJC Scopus subject areas

- Computer Science Applications
- Information Systems

## Cite this

Nogami, Y., Tada, K., & Uehara, S. (2014). An efficient generation of geometric sequences defined with trace and legendre symbol. In

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