The Cross-Correlation of Binary Sequences With Optimal Autocorrelation

Binary sequences with low correlation have applications in communication systems and cryptography. Though binary sequences with optimal autocorrelation were constructed in the literature, no pair of binary sequences with optimal autocorrelation are known to have also best possible cross correlation. In this paper, new bounds on the cross correlation of binary sequences with optimal autocorrelation are derived, and pairs of binary sequences having optimal autocorrelation and meeting some of these bounds are presented. These new bounds are better than the Sarwate bounds on the cross correlation of binary sequences with optimal autocorrelation.

[1]  Cunsheng Ding,et al.  Almost difference sets and their sequences with optimal autocorrelation , 2001, IEEE Trans. Inf. Theory.

[2]  Hans D. Schotten,et al.  Binary and quadriphase sequences with optimal autocorrelation properties: a survey , 2003, IEEE Trans. Inf. Theory.

[3]  Cunsheng Ding,et al.  Autocorrelation Values of Generalized Cyclotomic Sequences of Order Two , 1998, IEEE Trans. Inf. Theory.

[4]  S. Chowla,et al.  On Difference Sets. , 1949, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Dilip V. Sarwate,et al.  Bounds on crosscorrelation and autocorrelation of sequences (Corresp.) , 1979, IEEE Transactions on Information Theory.

[6]  Mark Goresky,et al.  Correlation Functions of Geometric Sequences , 1991, EUROCRYPT.

[7]  Edward Spence,et al.  A Family of Difference Sets , 1977, J. Comb. Theory, Ser. A.

[8]  Pingzhi Fan,et al.  SEQUENCE DESIGN FOR COMMUNICATIONS APPLICATIONS , 1996 .

[9]  A. Robert Calderbank,et al.  On a conjecture of Helleseth regarding pairs of binary m-sequences , 1996, IEEE Trans. Inf. Theory.

[10]  Tor Helleseth,et al.  Some results about the cross-correlation function between two maximal linear sequences , 1976, Discret. Math..

[11]  Doreen Hertel.  Crosscorrelation between GMW and Dillon-Dobbertin Sequences , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[12]  A. Robert Calderbank,et al.  Proof of a conjecture of Sarwate and Pursley regarding pairs of binary m-sequences , 1995, IEEE Trans. Inf. Theory.

[13]  Stephan Mertens,et al.  On the ground states of the Bernasconi model , 1997 .

[14]  Dieter Jungnickel,et al.  Geometry, Combinatorial Designs and Related Structures: Difference sets: an update , 1997 .

[15]  T. Storer.  Cyclotomy and difference sets , 1967 .

[16]  Dieter Jungnickel,et al.  Difference Sets: An Introduction , 1999 .

[17]  Guang Gong,et al.  Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar , 2005 .

[18]  Dieter Jungnickel,et al.  Perfect and Almost Perfect Sequences , 1999, Discret. Appl. Math..

[19]  Markus Antweiler.  Cross-correlation of p-ary GMW sequences , 1994, IEEE Trans. Inf. Theory.

[20]  Tom Høholdt,et al.  The merit factor of binary sequences related to difference sets , 1991, IEEE Trans. Inf. Theory.

[21]  Cunsheng Ding,et al.  Several classes of binary sequences with three-level autocorrelation , 1999, IEEE Trans. Inf. Theory.

[22]  M.B. Pursley,et al.  Crosscorrelation properties of pseudorandom and related sequences , 1980, Proceedings of the IEEE.

[23]  Cunsheng Ding,et al.  Binary sequences with optimal autocorrelation , 2009, Theor. Comput. Sci..

[24]  Cunsheng Ding,et al.  Sets of Optimal Frequency-Hopping Sequences , 2008, IEEE Transactions on Information Theory.