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.
Recommended Citation
Yasuyuki Nogami, Satoshi Uehara, Kazuyoshi Tsuchiya, Nasima Begum, Hiroto Ino, and Robert Morelos-Zaragoza. "A Multi-Value Sequence Generated by Power Residue Symbol and Trace Function over Odd Characteristic Field" IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (2016): 2226-2237. https://doi.org/10.1587/transfun.E99.A.2226
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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