## Abstract

In this paper, the authors have proposed a new approach for generating multi-value sequence by utilizing primitive element, trace function, and k-th power residue symbol over odd characteristic field. Let p be an odd prime and F_{p} be an odd characteristic prime field, m be the degree of the primitive polynomial f(x), and k be a prime factor of p - 1. In details, the procedure for generating multi-value sequence is as follows: primitive polynomial f(x) generates maximum length vector sequence, then trace function Tr(·) maps an element of extension field F_{p}m to an element of prime field F_{p}, next non-zero scalar A € F_{p} is added to the trace value, and finally k-th power residue symbol is utilized to map the scalars into (k + 1) values multi-value sequence. In this method, a certain mapping function M_{k}(·) is utilized during the autocorrelation calculation. Hence, our proposed multi-value sequence has some parameters such as p, m, k, and A. This paper discusses the period, autocorrelation, and cross-correlation properties of proposed multi-value sequence based on some experimental results.

Original language | English |
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Title of host publication | Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 604-609 |

Number of pages | 6 |

ISBN (Electronic) | 9781509026555 |

DOIs | |

Publication status | Published - Jan 13 2017 |

Event | 4th International Symposium on Computing and Networking, CANDAR 2016 - Hiroshima, Japan Duration: Nov 22 2016 → Nov 25 2016 |

### Other

Other | 4th International Symposium on Computing and Networking, CANDAR 2016 |
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Country | Japan |

City | Hiroshima |

Period | 11/22/16 → 11/25/16 |

## ASJC Scopus subject areas

- Computer Science Applications
- Hardware and Architecture
- Signal Processing
- Computer Networks and Communications