Abstract
In this paper, the authors have proposed a new approach for generating multi-value sequence by utilizing primitive element, trace function, and k-th power residue symbol over odd characteristic field. Let p be an odd prime and Fp be an odd characteristic prime field, m be the degree of the primitive polynomial f(x), and k be a prime factor of p - 1. In details, the procedure for generating multi-value sequence is as follows: primitive polynomial f(x) generates maximum length vector sequence, then trace function Tr(·) maps an element of extension field Fpm to an element of prime field Fp, next non-zero scalar A € Fp is added to the trace value, and finally k-th power residue symbol is utilized to map the scalars into (k + 1) values multi-value sequence. In this method, a certain mapping function Mk(·) is utilized during the autocorrelation calculation. Hence, our proposed multi-value sequence has some parameters such as p, m, k, and A. This paper discusses the period, autocorrelation, and cross-correlation properties of proposed multi-value sequence based on some experimental results.
| Original language | English |
|---|---|
| Title of host publication | Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 604-609 |
| Number of pages | 6 |
| ISBN (Electronic) | 9781509026555 |
| DOIs | |
| Publication status | Published - Jan 13 2017 |
| Event | 4th International Symposium on Computing and Networking, CANDAR 2016 - Hiroshima, Japan Duration: Nov 22 2016 → Nov 25 2016 |
Other
| Other | 4th International Symposium on Computing and Networking, CANDAR 2016 |
|---|---|
| Country | Japan |
| City | Hiroshima |
| Period | 11/22/16 → 11/25/16 |
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ASJC Scopus subject areas
- Computer Science Applications
- Hardware and Architecture
- Signal Processing
- Computer Networks and Communications
Cite this
Auto and cross correlation of well balanced sequence over odd characteristic field. / Arshad, Ali Md; Nogami, Yasuyuki; Ino, Hiroto; Uehara, Satoshi.
Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016. Institute of Electrical and Electronics Engineers Inc., 2017. p. 604-609 7818679.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Auto and cross correlation of well balanced sequence over odd characteristic field
AU - Arshad, Ali Md
AU - Nogami, Yasuyuki
AU - Ino, Hiroto
AU - Uehara, Satoshi
PY - 2017/1/13
Y1 - 2017/1/13
N2 - In this paper, the authors have proposed a new approach for generating multi-value sequence by utilizing primitive element, trace function, and k-th power residue symbol over odd characteristic field. Let p be an odd prime and Fp be an odd characteristic prime field, m be the degree of the primitive polynomial f(x), and k be a prime factor of p - 1. In details, the procedure for generating multi-value sequence is as follows: primitive polynomial f(x) generates maximum length vector sequence, then trace function Tr(·) maps an element of extension field Fpm to an element of prime field Fp, next non-zero scalar A € Fp is added to the trace value, and finally k-th power residue symbol is utilized to map the scalars into (k + 1) values multi-value sequence. In this method, a certain mapping function Mk(·) is utilized during the autocorrelation calculation. Hence, our proposed multi-value sequence has some parameters such as p, m, k, and A. This paper discusses the period, autocorrelation, and cross-correlation properties of proposed multi-value sequence based on some experimental results.
AB - In this paper, the authors have proposed a new approach for generating multi-value sequence by utilizing primitive element, trace function, and k-th power residue symbol over odd characteristic field. Let p be an odd prime and Fp be an odd characteristic prime field, m be the degree of the primitive polynomial f(x), and k be a prime factor of p - 1. In details, the procedure for generating multi-value sequence is as follows: primitive polynomial f(x) generates maximum length vector sequence, then trace function Tr(·) maps an element of extension field Fpm to an element of prime field Fp, next non-zero scalar A € Fp is added to the trace value, and finally k-th power residue symbol is utilized to map the scalars into (k + 1) values multi-value sequence. In this method, a certain mapping function Mk(·) is utilized during the autocorrelation calculation. Hence, our proposed multi-value sequence has some parameters such as p, m, k, and A. This paper discusses the period, autocorrelation, and cross-correlation properties of proposed multi-value sequence based on some experimental results.
UR - http://www.scopus.com/inward/record.url?scp=85015215662&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85015215662&partnerID=8YFLogxK
U2 - 10.1109/CANDAR.2016.30
DO - 10.1109/CANDAR.2016.30
M3 - Conference contribution
AN - SCOPUS:85015215662
SP - 604
EP - 609
BT - Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016
PB - Institute of Electrical and Electronics Engineers Inc.
ER -