Document Type


Publication Date

April 2017


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.


Copyright 2017 The Institute of Electronics, Information and Communication Engineers
This article was published in IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, volume E100-A, number 4, April 2017. This article can also be found online at this link. It is included here with the publisher's permission.