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Multi-Valued Sequences Generated By Power Residue Symbols Over Odd Characteristic Fields, Begum Nasima, Yasuyuki Nogami, Satoshi Uehara, Robert Morelos-Zaragoza

Faculty Publications

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 …