### Abstract

This paper proposes a new approach for generating pseudo random multi-valued (including binary-valued) sequences. The approach uses a primitive polynomial over an odd characteristic prime field F_{p}, where p is an odd prime number. Then, for the maximum length sequence of vectors generated by the primitive polynomial, the trace function is used for mapping these vectors to scalars as elements in the prime field. Power residue symbol (Legendre symbol in binary case) is applied to translate the scalars to k-value scalars, where k is a prime factor of p-1. Finally, a pseudo random k-value sequence is obtained. Some important properties of the resulting multi-valued sequences are shown, such as their period, autocorrelation, and linear complexity together with their proofs and small examples.

Original language | English |
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Pages (from-to) | 922-929 |

Number of pages | 8 |

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

Volume | E100A |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 1 2017 |

### Keywords

- Geometric sequence
- Legendre symbol
- Multi-valued sequence
- Odd characteristic
- Primitive polynomial
- Trace

### ASJC Scopus subject areas

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

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## Cite this

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

*E100A*(4), 922-929. https://doi.org/10.1587/transfun.E100.A.922