Multi-Valued Sequences Generated by Power Residue Symbols over Odd Characteristic Fields
Summary :
This paper proposes a new approach for generating pseudo random multi-valued (including binary-valued) sequences. The approach uses a primitive polynomial over an odd characteristic prime field $ {p}$, where p is an odd prime number. Then, for the maximum length sequence of vectors generated by the primitive polynomial, the trace function is used for mapping these vectors to scalars as elements in the prime field. Power residue symbol (Legendre symbol in binary case) is applied to translate the scalars to k-value scalars, where k is a prime factor of p-1. Finally, a pseudo random k-value sequence is obtained. Some important properties of the resulting multi-valued sequences are shown, such as their period, autocorrelation, and linear complexity together with their proofs and small examples.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.4 pp.922-929
- Publication Date
- 2017/04/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E100.A.922
- Type of Manuscript
- Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)
- Category
- Sequences
Authors
Begum NASIMA
University of Asia Pacific
Yasuyuki NOGAMI
Okayama University
Satoshi UEHARA
The University of Kitakyushu
Robert H. MOLEROS-ZARAGOZA
San Jose State University
Keyword
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Begum NASIMA, Yasuyuki NOGAMI, Satoshi UEHARA, Robert H. MOLEROS-ZARAGOZA, "Multi-Valued Sequences Generated by Power Residue Symbols over Odd Characteristic Fields" in IEICE TRANSACTIONS on Fundamentals,
vol. E100-A, no. 4, pp. 922-929, April 2017, doi: 10.1587/transfun.E100.A.922.
Abstract: This paper proposes a new approach for generating pseudo random multi-valued (including binary-valued) sequences. The approach uses a primitive polynomial over an odd characteristic prime field $ {p}$, where p is an odd prime number. Then, for the maximum length sequence of vectors generated by the primitive polynomial, the trace function is used for mapping these vectors to scalars as elements in the prime field. Power residue symbol (Legendre symbol in binary case) is applied to translate the scalars to k-value scalars, where k is a prime factor of p-1. Finally, a pseudo random k-value sequence is obtained. Some important properties of the resulting multi-valued sequences are shown, such as their period, autocorrelation, and linear complexity together with their proofs and small examples.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.922/_p
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@ARTICLE{e100-a_4_922,
author={Begum NASIMA, Yasuyuki NOGAMI, Satoshi UEHARA, Robert H. MOLEROS-ZARAGOZA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Multi-Valued Sequences Generated by Power Residue Symbols over Odd Characteristic Fields},
year={2017},
volume={E100-A},
number={4},
pages={922-929},
abstract={This paper proposes a new approach for generating pseudo random multi-valued (including binary-valued) sequences. The approach uses a primitive polynomial over an odd characteristic prime field $ {p}$, where p is an odd prime number. Then, for the maximum length sequence of vectors generated by the primitive polynomial, the trace function is used for mapping these vectors to scalars as elements in the prime field. Power residue symbol (Legendre symbol in binary case) is applied to translate the scalars to k-value scalars, where k is a prime factor of p-1. Finally, a pseudo random k-value sequence is obtained. Some important properties of the resulting multi-valued sequences are shown, such as their period, autocorrelation, and linear complexity together with their proofs and small examples.},
keywords={},
doi={10.1587/transfun.E100.A.922},
ISSN={1745-1337},
month={April},}
Copy
TY - JOUR
TI - Multi-Valued Sequences Generated by Power Residue Symbols over Odd Characteristic Fields
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 922
EP - 929
AU - Begum NASIMA
AU - Yasuyuki NOGAMI
AU - Satoshi UEHARA
AU - Robert H. MOLEROS-ZARAGOZA
PY - 2017
DO - 10.1587/transfun.E100.A.922
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2017
AB - This paper proposes a new approach for generating pseudo random multi-valued (including binary-valued) sequences. The approach uses a primitive polynomial over an odd characteristic prime field $ {p}$, where p is an odd prime number. Then, for the maximum length sequence of vectors generated by the primitive polynomial, the trace function is used for mapping these vectors to scalars as elements in the prime field. Power residue symbol (Legendre symbol in binary case) is applied to translate the scalars to k-value scalars, where k is a prime factor of p-1. Finally, a pseudo random k-value sequence is obtained. Some important properties of the resulting multi-valued sequences are shown, such as their period, autocorrelation, and linear complexity together with their proofs and small examples.
ER -
English
