IEICE TRANSACTIONS on Fundamentals
A Multi-Value Sequence Generated by Power Residue Symbol and Trace Function over Odd Characteristic Field
Summary :
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 $F{p}{m} ightarrow {p}$, A is a non-zero scalar in the prime field $ {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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.12 pp.2226-2237
- Publication Date
- 2016/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E99.A.2226
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Sequences
Authors
Yasuyuki NOGAMI
Okayama University
Satoshi UEHARA
The University of Kitakyushu
Kazuyoshi TSUCHIYA
Koden Electronics Co. Ltd.
Nasima BEGUM
Okayama University
Hiroto INO
Okayama University
Robert H. MOLEROS-ZARAGOZA
San Jose State University
Keyword
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Yasuyuki NOGAMI, Satoshi UEHARA, Kazuyoshi TSUCHIYA, Nasima BEGUM, Hiroto INO, Robert H. MOLEROS-ZARAGOZA, "A Multi-Value Sequence Generated by Power Residue Symbol and Trace Function over Odd Characteristic Field" in IEICE TRANSACTIONS on Fundamentals,
vol. E99-A, no. 12, pp. 2226-2237, December 2016, 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 $F{p}{m}
ightarrow {p}$, A is a non-zero scalar in the prime field $ {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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.2226/_p
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@ARTICLE{e99-a_12_2226,
author={Yasuyuki NOGAMI, Satoshi UEHARA, Kazuyoshi TSUCHIYA, Nasima BEGUM, Hiroto INO, Robert H. MOLEROS-ZARAGOZA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Multi-Value Sequence Generated by Power Residue Symbol and Trace Function over Odd Characteristic Field},
year={2016},
volume={E99-A},
number={12},
pages={2226-2237},
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 $F{p}{m}
ightarrow {p}$, A is a non-zero scalar in the prime field $ {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.},
keywords={},
doi={10.1587/transfun.E99.A.2226},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - A Multi-Value Sequence Generated by Power Residue Symbol and Trace Function over Odd Characteristic Field
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2226
EP - 2237
AU - Yasuyuki NOGAMI
AU - Satoshi UEHARA
AU - Kazuyoshi TSUCHIYA
AU - Nasima BEGUM
AU - Hiroto INO
AU - Robert H. MOLEROS-ZARAGOZA
PY - 2016
DO - 10.1587/transfun.E99.A.2226
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2016
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 | 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 $F{p}{m}
ightarrow {p}$, A is a non-zero scalar in the prime field $ {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.
ER -
English
