MultiValued Sequences Generated by Power Residue Symbols over Odd Characteristic Fields
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Abstract
<p>This paper proposes a new approach for generating pseudo random multivalued (including binaryvalued) sequences. The approach uses a primitive polynomial over an odd characteristic prime field $\f{p}$, where <i>p</i> 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 <i>k</i>value scalars, where <i>k</i> is a prime factor of <i>p</i>1. Finally, a pseudo random <i>k</i>value sequence is obtained. Some important properties of the resulting multivalued sequences are shown, such as their period, autocorrelation, and linear complexity together with their proofs and small examples.</p>
Journal

 IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E100.A(4), 922929, 2017
The Institute of Electronics, Information and Communication Engineers