TY - JOUR

T1 - Multi-valued sequences generated by power residue symbols over odd characteristic fields

AU - Nasima, Begum

AU - Nogami, Yasuyuki

AU - Uehara, Satoshi

AU - Moleros-Zaragoza, Robert H.

N1 - Publisher Copyright:
Copyright © 2017 The Institute of Electronics, Information and Communication Engineers.

PY - 2017/4

Y1 - 2017/4

N2 - 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 Fp, 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.

AB - 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 Fp, 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.

KW - Geometric sequence

KW - Legendre symbol

KW - Multi-valued sequence

KW - Odd characteristic

KW - Primitive polynomial

KW - Trace

UR - http://www.scopus.com/inward/record.url?scp=85017391480&partnerID=8YFLogxK

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U2 - 10.1587/transfun.E100.A.922

DO - 10.1587/transfun.E100.A.922

M3 - Article

AN - SCOPUS:85017391480

SN - 0916-8508

VL - E100A

SP - 922

EP - 929

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

IS - 4

ER -