### 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 |
---|---|

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 |
---|---|

Country | Japan |

City | Hiroshima |

Period | 11/22/16 → 11/25/16 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016*(pp. 604-609). [7818679] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CANDAR.2016.30

**Auto and cross correlation of well balanced sequence over odd characteristic field.** / Arshad, Ali Md; Nogami, Yasuyuki; Ino, Hiroto; Uehara, Satoshi.

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

*Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016.*, 7818679, Institute of Electrical and Electronics Engineers Inc., pp. 604-609, 4th International Symposium on Computing and Networking, CANDAR 2016, Hiroshima, Japan, 11/22/16. https://doi.org/10.1109/CANDAR.2016.30

}

TY - GEN

T1 - Auto and cross correlation of well balanced sequence over odd characteristic field

AU - Arshad, Ali Md

AU - Nogami, Yasuyuki

AU - Ino, Hiroto

AU - Uehara, Satoshi

PY - 2017/1/13

Y1 - 2017/1/13

N2 - 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 Fp 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 Fpm to an element of prime field Fp, next non-zero scalar A € Fp 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 Mk(·) 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.

AB - 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 Fp 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 Fpm to an element of prime field Fp, next non-zero scalar A € Fp 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 Mk(·) 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.

UR - http://www.scopus.com/inward/record.url?scp=85015215662&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015215662&partnerID=8YFLogxK

U2 - 10.1109/CANDAR.2016.30

DO - 10.1109/CANDAR.2016.30

M3 - Conference contribution

AN - SCOPUS:85015215662

SP - 604

EP - 609

BT - Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -