### 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 |

### 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

## Fingerprint Dive into the research topics of 'A multi-value sequence generated by power residue symbol and trace function over odd characteristic field'. Together they form a unique fingerprint.

## 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