Document Type

Article

Publication Date

December 2016

Publication Title

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volume

E99. A

Issue Number

12

First Page

2226

Last Page

2237

DOI

10.1587/transfun.E99.A.2226

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 | ti=fk(Tr(ωi)+A)}, where ω is a primitive element in the extension field $\F{p}{m}$, Tr(⋅) is the trace function that maps $\F{p}{m} \rightarrow \f{p}$, A is a non-zero scalar in the prime field $\f{p}$, 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.

Comments

This article was originally published in IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, volume E99. A, issue 12, 2016. ©2016 IEICE This article is also available online at http://dx.doi.org/10.1587/transfun.E99.A.2226
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