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

N1 - Publisher Copyright:
© 2016 IEEE.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

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.

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U2 - 10.1109/CANDAR.2016.30

DO - 10.1109/CANDAR.2016.30

M3 - Conference contribution

AN - SCOPUS:85015215662

T3 - Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016

SP - 604

EP - 609

BT - Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 4th International Symposium on Computing and Networking, CANDAR 2016

Y2 - 22 November 2016 through 25 November 2016

ER -