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.
N1 - Publisher Copyright:
Copyright © 2016 The Institute of Electronics, Information and Communication Engineers.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2016/12
Y1 - 2016/12
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 Fpm, Tr(·) is the trace function that maps Fpm → 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 Fpm, Tr(·) is the trace function that maps Fpm → 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
UR - http://www.scopus.com/inward/record.url?scp=84999232843&partnerID=8YFLogxK
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
AN - SCOPUS:84999232843
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 -