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 language | English |
|---|---|
| Pages (from-to) | 2226-2237 |
| Number of pages | 12 |
| Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
| Volume | E99A |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - Dec 1 2016 |
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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
Cite this
A multi-value sequence generated by power residue symbol and trace function over odd characteristic field. / Nogami, Yasuyuki; Uehara, Satoshi; Tsuchiya, Kazuyoshi; Begum, Nasima; Ino, Hiroto; Moleros-Zaragoza, Robert H.
In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E99A, No. 12, 01.12.2016, p. 2226-2237.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A multi-value sequence generated by power residue symbol and trace function over odd characteristic field
AU - Nogami, Yasuyuki
AU - Uehara, Satoshi
AU - Tsuchiya, Kazuyoshi
AU - Begum, Nasima
AU - Ino, Hiroto
AU - Moleros-Zaragoza, Robert H.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - 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.
AB - 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.
KW - Cross-correlation
KW - Multi-value sequence
KW - Odd characteristic
KW - Power residue symbol
KW - Primitive polynomial
KW - Trace
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UR - http://www.scopus.com/inward/citedby.url?scp=84999232843&partnerID=8YFLogxK
U2 - 10.1587/transfun.E99.A.2226
DO - 10.1587/transfun.E99.A.2226
M3 - Article
VL - E99A
SP - 2226
EP - 2237
JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
SN - 0916-8508
IS - 12
ER -