Autocorrelation of Legendre–Sidelnikov Sequences

Author

Su, Ming ; Winterhof, Arne

Author_Institution

Dept. of Comput. Sci., Nankai Univ., Tianjin, China

Volume

56

Issue

4

fYear

2010

fDate

4/1/2010 12:00:00 AM

Firstpage

1714

Lastpage

1718

Abstract

We combine the concepts of the p-periodic Legendre sequence, the (q-1)-periodic Sidelnikov sequence and the two-prime generator to introduce a new p(q-1)-periodic sequence called Legendre-Sidelnikov sequence. We show that this new sequence is balanced if p=q. For an arbitrary odd prime p and an arbitrary power q of an odd prime with gcd (p,q-1)=1 we determine the exact values of its (periodic) autocorrelation function and deduce an upper bound on its aperiodic autocorrelation function showing that it is small compared to its period.

Keywords

Legendre polynomials; correlation theory; sequences; -periodic Legendre sequence; Legendre-Sidelnikov sequences; aperiodic autocorrelation function; autocorrelation; autocorrelation function; Autocorrelation; Binary sequences; Character generation; Computer science education; Cryptography; Galois fields; Length measurement; Random sequences; Upper bound; Wireless communication; Autocorrelation; Legendre sequence; Sidelnikov sequence; binary sequences; cryptography; finite fields; quadratic character (Legendre symbol); two-prime generator; wireless communication;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2010.2040893

Filename

5437432