Article
Multi-Valued Sequences Generated by Power Residue Symbols over Odd Characteristic Fields
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
(2017)
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.
Keywords
- geometric sequence,
- multi-valued sequence,
- odd characteristic,
- primitive polynomial,
- Legendre symbol,
- trace
Disciplines
Publication Date
April 1, 2017
DOI
10.1587/transfun.E100.A.922
Publisher Statement
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.
Citation Information
Begum Nasima, Yasuyuki Nogami, Satoshi Uehara and Robert H Morelos-Zaragoza. "Multi-Valued Sequences Generated by Power Residue Symbols over Odd Characteristic Fields" IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Vol. E100.A Iss. 4 (2017) p. 922 - 929 ISSN: 0916-8508 Available at: http://works.bepress.com/robert_morelos-zaragoza/48/