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.
@article{ITA_2013__47_4_371_0,
author = {WANG, Huijuan and WEN, Qiaoyan and ZHANG, Jie},
title = {GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {47},
year = {2013},
pages = {371-388},
doi = {10.1051/ita/2013043},
mrnumber = {3132297},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2013__47_4_371_0}
}
WANG, Huijuan; WEN, Qiaoyan; ZHANG, Jie. GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 47 (2013) pp. 371-388. doi : 10.1051/ita/2013043. http://gdmltest.u-ga.fr/item/ITA_2013__47_4_371_0/
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