RAIRO-Theor. Inf. Appl.
Volume 47, Number 4, October-December 2013
|Page(s)||371 - 388|
|Published online||12 November 2013|
GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation∗
1 The author is with the State Key
Laboratory of Networking and Switching Technology, Beijing University of Posts and
2 The author is with the State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, 100876 Beijing, P.R. China
3 The author is with School of Science, Beijing University of Posts and Telecommunications, 100876 Beijing, P.R. China
Accepted: 26 September 2013
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.
Mathematics Subject Classification: 11T71 / 14G50 / 94A60
Key words: Arithmetic cross-correlation / Legendre symbol / primitive sequence / cyclically distinct
© EDP Sciences 2013
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