Ensembles of sequences and arrays

Ensembles of periodic binary sequences with low off-peak autocorrelation and cross-correlation are highly valued and difficult to find. The small Kasami, Kamaletdinov 1&2, and Rational Cycle are versatile, because they can be converted into Costas-like arrays for frequency/time hopping. We present a unified construction of such ensembles using linear feedback shift registers.

[1]  B. Elspas,et al.  The Theory of Autonomous Linear Sequential Networks , 1959 .

[2]  Oscar Moreno,et al.  New Optimal Low Correlation Sequences for Wireless Communications , 2012, SETA.

[3]  Marlin P. Ristenbatt,et al.  Introduction to linear shift-register generated sequences , 1958 .

[4]  T. Kasami WEIGHT DISTRIBUTION FORMULA FOR SOME CLASS OF CYCLIC CODES , 1966 .

[5]  Andrew Z. Tirkel,et al.  Matrix construction using cyclic shifts of a column , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[6]  M. Stular,et al.  Maximum periodic correlation of pseudo-random sequences in CDMA , 2000, 2000 10th Mediterranean Electrotechnical Conference. Information Technology and Electrotechnology for the Mediterranean Countries. Proceedings. MeleCon 2000 (Cat. No.00CH37099).

[7]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[8]  Oscar Moreno,et al.  Secure CDMA and Frequency Hop Sequences , 2013, ISWCS.

[9]  Marvin K. Simon,et al.  Spread Spectrum Communications Handbook , 1994 .

[10]  Oscar Moreno,et al.  A new family of frequency-hop codes , 2000, IEEE Trans. Commun..

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

[12]  S. K. Amarasinghe,et al.  Families of sequences and arrays with good periodic correlation properties , 1991 .