GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation

Huijuan WANG; Qiaoyan WEN; Jie ZHANG

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2013)

  • Volume: 47, Issue: 4, page 371-388
  • ISSN: 0988-3754

Abstract

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The Legendre symbol has been used to construct sequences with ideal cross-correlation, but it was never used in the arithmetic cross-correlation. In this paper, a new class of generalized Legendre sequences are described and analyzed with respect to their period, distributional, arithmetic cross-correlation and distinctness properties. This analysis gives a new approach to study the connection between the Legendre symbol and the arithmetic cross-correlation. In the end of this paper, possible application of these sequences with optimal arithmetic cross-correlation is indicated.

How to cite

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WANG, Huijuan, WEN, Qiaoyan, and ZHANG, Jie. "GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 47.4 (2013): 371-388. <http://eudml.org/doc/272999>.

@article{WANG2013,
abstract = {The Legendre symbol has been used to construct sequences with ideal cross-correlation, but it was never used in the arithmetic cross-correlation. In this paper, a new class of generalized Legendre sequences are described and analyzed with respect to their period, distributional, arithmetic cross-correlation and distinctness properties. This analysis gives a new approach to study the connection between the Legendre symbol and the arithmetic cross-correlation. In the end of this paper, possible application of these sequences with optimal arithmetic cross-correlation is indicated.},
author = {WANG, Huijuan, WEN, Qiaoyan, ZHANG, Jie},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {arithmetic cross-correlation; Legendre symbol; primitive sequence; cyclically distinct},
language = {eng},
number = {4},
pages = {371-388},
publisher = {EDP-Sciences},
title = {GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation},
url = {http://eudml.org/doc/272999},
volume = {47},
year = {2013},
}

TY - JOUR
AU - WANG, Huijuan
AU - WEN, Qiaoyan
AU - ZHANG, Jie
TI - GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 4
SP - 371
EP - 388
AB - The Legendre symbol has been used to construct sequences with ideal cross-correlation, but it was never used in the arithmetic cross-correlation. In this paper, a new class of generalized Legendre sequences are described and analyzed with respect to their period, distributional, arithmetic cross-correlation and distinctness properties. This analysis gives a new approach to study the connection between the Legendre symbol and the arithmetic cross-correlation. In the end of this paper, possible application of these sequences with optimal arithmetic cross-correlation is indicated.
LA - eng
KW - arithmetic cross-correlation; Legendre symbol; primitive sequence; cyclically distinct
UR - http://eudml.org/doc/272999
ER -

References

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  14. [14] Huijuan WANG, Qiaoyan WEN and Jie ZHANG, 2-Adic Complexity of Self-shrinking Sequence. IEEE Trans. Fundamentals E94-A (2011) 11. 
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