A multi-value sequence generated by power residue symbol and trace function over odd characteristic field

Yasuyuki Nogami, Satoshi Uehara, Kazuyoshi Tsuchiya, Nasima Begum, Hiroto Ino, Robert H. Moleros-Zaragoza

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

This paper proposes a new multi-value sequence generated by utilizing primitive element, trace, and power residue symbol over odd characteristic finite field. In detail, let p and k be an odd prime number as the characteristic and a prime factor of p - 1, respectively. Our proposal generates k-value sequence T = ti j ti = fk(Tr(ωi) + A), where ω is a primitive element in the extension field Fp m, Tr(·) is the trace function that maps Fp m → Fp, A is a non-zero scalar in the prime field Fp, and fk(·) is a certain mapping function based on k-th power residue symbol. Thus, the proposed sequence has four parameters as p, m, k, and A.Then, this paper theoretically shows its period, autocorrelation, and cross-correlation. In addition, this paper discusses its linear complexity based on experimental results. Then, these features of the proposed sequence are observed with some examples.

Original languageEnglish
Pages (from-to)2226-2237
Number of pages12
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE99A
Issue number12
DOIs
Publication statusPublished - Dec 1 2016

Keywords

  • Cross-correlation
  • Multi-value sequence
  • Odd characteristic
  • Power residue symbol
  • Primitive polynomial
  • Trace

ASJC Scopus subject areas

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

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