### Abstract

This paper proposes a new multi-value sequence generated by utilizing primitive element, trace, and power residue symbol over odd characteristic finite field. In detail, let p and k be an odd prime number as the characteristic and a prime factor of p - 1, respectively. Our proposal generates k-value sequence T = t_{i} j t_{i} = f_{k}(Tr(ω^{i}) + A), where ω is a primitive element in the extension field F_{p} ^{m}, Tr(·) is the trace function that maps F_{p} ^{m} → F_{p}, A is a non-zero scalar in the prime field F_{p}, and f_{k}(·) is a certain mapping function based on k-th power residue symbol. Thus, the proposed sequence has four parameters as p, m, k, and A.Then, this paper theoretically shows its period, autocorrelation, and cross-correlation. In addition, this paper discusses its linear complexity based on experimental results. Then, these features of the proposed sequence are observed with some examples.

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

Pages (from-to) | 2226-2237 |

Number of pages | 12 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E99A |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 1 2016 |

### Fingerprint

### Keywords

- Cross-correlation
- Multi-value sequence
- Odd characteristic
- Power residue symbol
- Primitive polynomial
- Trace

### ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E99A*(12), 2226-2237. https://doi.org/10.1587/transfun.E99.A.2226

**A multi-value sequence generated by power residue symbol and trace function over odd characteristic field.** / Nogami, Yasuyuki; Uehara, Satoshi; Tsuchiya, Kazuyoshi; Begum, Nasima; Ino, Hiroto; Moleros-Zaragoza, Robert H.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E99A, no. 12, pp. 2226-2237. https://doi.org/10.1587/transfun.E99.A.2226

}

TY - JOUR

T1 - A multi-value sequence generated by power residue symbol and trace function over odd characteristic field

AU - Nogami, Yasuyuki

AU - Uehara, Satoshi

AU - Tsuchiya, Kazuyoshi

AU - Begum, Nasima

AU - Ino, Hiroto

AU - Moleros-Zaragoza, Robert H.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - This paper proposes a new multi-value sequence generated by utilizing primitive element, trace, and power residue symbol over odd characteristic finite field. In detail, let p and k be an odd prime number as the characteristic and a prime factor of p - 1, respectively. Our proposal generates k-value sequence T = ti j ti = fk(Tr(ωi) + A), where ω is a primitive element in the extension field Fp m, Tr(·) is the trace function that maps Fp m → Fp, A is a non-zero scalar in the prime field Fp, and fk(·) is a certain mapping function based on k-th power residue symbol. Thus, the proposed sequence has four parameters as p, m, k, and A.Then, this paper theoretically shows its period, autocorrelation, and cross-correlation. In addition, this paper discusses its linear complexity based on experimental results. Then, these features of the proposed sequence are observed with some examples.

AB - This paper proposes a new multi-value sequence generated by utilizing primitive element, trace, and power residue symbol over odd characteristic finite field. In detail, let p and k be an odd prime number as the characteristic and a prime factor of p - 1, respectively. Our proposal generates k-value sequence T = ti j ti = fk(Tr(ωi) + A), where ω is a primitive element in the extension field Fp m, Tr(·) is the trace function that maps Fp m → Fp, A is a non-zero scalar in the prime field Fp, and fk(·) is a certain mapping function based on k-th power residue symbol. Thus, the proposed sequence has four parameters as p, m, k, and A.Then, this paper theoretically shows its period, autocorrelation, and cross-correlation. In addition, this paper discusses its linear complexity based on experimental results. Then, these features of the proposed sequence are observed with some examples.

KW - Cross-correlation

KW - Multi-value sequence

KW - Odd characteristic

KW - Power residue symbol

KW - Primitive polynomial

KW - Trace

UR - http://www.scopus.com/inward/record.url?scp=84999232843&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84999232843&partnerID=8YFLogxK

U2 - 10.1587/transfun.E99.A.2226

DO - 10.1587/transfun.E99.A.2226

M3 - Article

AN - SCOPUS:84999232843

VL - E99A

SP - 2226

EP - 2237

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 12

ER -