Approximate Odd Periodic Correlation Distributions of Binary Sequences

Shinya MATSUFUJI; Kyoki IMAMURA

Approximate Odd Periodic Correlation Distributions of Binary Sequences

Shinya MATSUFUJI, Kyoki IMAMURA

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An approximate equation of the odd periodic correlation distribution for the family of binary sequences is derived from the exact even periodic correlation distribution. The distribution means the probabilities of correlation values which appear among all the phase-shifted sequences in the family. It is shown that the approximate distribution is almost the same as the computational result of some family such as the Gold sequences with low even periodic correlation magnitudes, or the Kasami sequences, the bent sequences with optimal even periodic correlation properties in the sense of the Welch's lower bound. It is also shown that the odd periodic correlation distribution of the family with optimal periodic correlation properties is not the Gaussian distribution, but that of the family of the Gold sequences with short period seems to be similar to the Gaussian distribution.

Publication: IEICE TRANSACTIONS on Communications Vol.E76-B No.8 pp.842-847

Publication Date: 1993/08/25

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Type of Manuscript: Special Section PAPER (Special Issue on Spread Spectrum Techniques and Applications)

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Shinya MATSUFUJI, Kyoki IMAMURA, "Approximate Odd Periodic Correlation Distributions of Binary Sequences" in IEICE TRANSACTIONS on Communications, vol. E76-B, no. 8, pp. 842-847, August 1993, doi: .
Abstract: An approximate equation of the odd periodic correlation distribution for the family of binary sequences is derived from the exact even periodic correlation distribution. The distribution means the probabilities of correlation values which appear among all the phase-shifted sequences in the family. It is shown that the approximate distribution is almost the same as the computational result of some family such as the Gold sequences with low even periodic correlation magnitudes, or the Kasami sequences, the bent sequences with optimal even periodic correlation properties in the sense of the Welch's lower bound. It is also shown that the odd periodic correlation distribution of the family with optimal periodic correlation properties is not the Gaussian distribution, but that of the family of the Gold sequences with short period seems to be similar to the Gaussian distribution.
URL: https://globals.ieice.org/en_transactions/communications/10.1587/e76-b_8_842/_p

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@ARTICLE{e76-b_8_842,
author={Shinya MATSUFUJI, Kyoki IMAMURA, },
journal={IEICE TRANSACTIONS on Communications},
title={Approximate Odd Periodic Correlation Distributions of Binary Sequences},
year={1993},
volume={E76-B},
number={8},
pages={842-847},
abstract={An approximate equation of the odd periodic correlation distribution for the family of binary sequences is derived from the exact even periodic correlation distribution. The distribution means the probabilities of correlation values which appear among all the phase-shifted sequences in the family. It is shown that the approximate distribution is almost the same as the computational result of some family such as the Gold sequences with low even periodic correlation magnitudes, or the Kasami sequences, the bent sequences with optimal even periodic correlation properties in the sense of the Welch's lower bound. It is also shown that the odd periodic correlation distribution of the family with optimal periodic correlation properties is not the Gaussian distribution, but that of the family of the Gold sequences with short period seems to be similar to the Gaussian distribution.},
keywords={},
doi={},
ISSN={},
month={August},}

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TY - JOUR
TI - Approximate Odd Periodic Correlation Distributions of Binary Sequences
T2 - IEICE TRANSACTIONS on Communications
SP - 842
EP - 847
AU - Shinya MATSUFUJI
AU - Kyoki IMAMURA
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Communications
SN -
VL - E76-B
IS - 8
JA - IEICE TRANSACTIONS on Communications
Y1 - August 1993
AB - An approximate equation of the odd periodic correlation distribution for the family of binary sequences is derived from the exact even periodic correlation distribution. The distribution means the probabilities of correlation values which appear among all the phase-shifted sequences in the family. It is shown that the approximate distribution is almost the same as the computational result of some family such as the Gold sequences with low even periodic correlation magnitudes, or the Kasami sequences, the bent sequences with optimal even periodic correlation properties in the sense of the Welch's lower bound. It is also shown that the odd periodic correlation distribution of the family with optimal periodic correlation properties is not the Gaussian distribution, but that of the family of the Gold sequences with short period seems to be similar to the Gaussian distribution.
ER -