## 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 |
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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 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
- Electrical and Electronic Engineering
- Applied Mathematics