A New Method to Compute Sequence Correlations Over Finite Fields

Serdar BOZTAŞ; Ferruh ÖZBUDAK; Eda TEKİN

doi:10.1587/transfun.2023SDP0009

A New Method to Compute Sequence Correlations Over Finite Fields

Serdar BOZTAŞ, Ferruh ÖZBUDAK, Eda TEKİN

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Summary :

In this paper we obtain a new method to compute the correlation values of two arbitrary sequences defined by a mapping from F_4ⁿ to F₄. We apply this method to demonstrate that the usual nonbinary maximal length sequences have almost ideal correlation under the canonical complex correlation definition and investigate some decimations giving good cross correlation. The techniques we develop are of independent interest for future investigation of sequence design and related problems, including Boolean functions.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.12 pp.1461-1469

Publication Date: 2023/12/01

Publicized: 2023/08/10

Online ISSN: 1745-1337

DOI: 10.1587/transfun.2023SDP0009

Type of Manuscript: Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)

Category: Cryptography and Information Security

Authors

Serdar BOZTAŞ
  University Research Foundation,RMIT University
Ferruh ÖZBUDAK
  Sabancı University
Eda TEKİN
  Karabük University

Keyword

CDMA, wireless communications, sequence design, correlation

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Serdar BOZTAŞ, Ferruh ÖZBUDAK, Eda TEKİN, "A New Method to Compute Sequence Correlations Over Finite Fields" in IEICE TRANSACTIONS on Fundamentals, vol. E106-A, no. 12, pp. 1461-1469, December 2023, doi: 10.1587/transfun.2023SDP0009.
Abstract: In this paper we obtain a new method to compute the correlation values of two arbitrary sequences defined by a mapping from F_4ⁿ to F₄. We apply this method to demonstrate that the usual nonbinary maximal length sequences have almost ideal correlation under the canonical complex correlation definition and investigate some decimations giving good cross correlation. The techniques we develop are of independent interest for future investigation of sequence design and related problems, including Boolean functions.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2023SDP0009/_p

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@ARTICLE{e106-a_12_1461,
author={Serdar BOZTAŞ, Ferruh ÖZBUDAK, Eda TEKİN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New Method to Compute Sequence Correlations Over Finite Fields},
year={2023},
volume={E106-A},
number={12},
pages={1461-1469},
abstract={In this paper we obtain a new method to compute the correlation values of two arbitrary sequences defined by a mapping from F_4ⁿ to F₄. We apply this method to demonstrate that the usual nonbinary maximal length sequences have almost ideal correlation under the canonical complex correlation definition and investigate some decimations giving good cross correlation. The techniques we develop are of independent interest for future investigation of sequence design and related problems, including Boolean functions.},
keywords={},
doi={10.1587/transfun.2023SDP0009},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - A New Method to Compute Sequence Correlations Over Finite Fields
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1461
EP - 1469
AU - Serdar BOZTAŞ
AU - Ferruh ÖZBUDAK
AU - Eda TEKİN
PY - 2023
DO - 10.1587/transfun.2023SDP0009
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2023
AB - In this paper we obtain a new method to compute the correlation values of two arbitrary sequences defined by a mapping from F_4ⁿ to F₄. We apply this method to demonstrate that the usual nonbinary maximal length sequences have almost ideal correlation under the canonical complex correlation definition and investigate some decimations giving good cross correlation. The techniques we develop are of independent interest for future investigation of sequence design and related problems, including Boolean functions.
ER -