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

Begum Nasima, Yasuyuki Nogami, Satoshi Uehara, Robert H. Moleros-Zaragoza

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)922-929
Number of pages8
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number4
Publication statusPublished - Apr 2017


  • Geometric sequence
  • Legendre symbol
  • Multi-valued sequence
  • Odd characteristic
  • Primitive polynomial
  • Trace

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


Dive into the research topics of 'Multi-valued sequences generated by power residue symbols over odd characteristic fields'. Together they form a unique fingerprint.

Cite this