Perfect Gaussian Integer Sequences of Arbitrary Length

In this work, we describe some methods to generate zero autocorrelation Gauss integer sequences of arbitrary length. These methods can be combined with each other so that more choices can be made.

[1]  Soo-Chang Pei,et al.  On integer-valued zero autocorrelation sequences , 2013, 2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference.

[2]  M. Schroeder.  Number Theory in Science and Communication , 1984 .

[3]  K. Williams,et al.  Gauss and Jacobi sums , 2021, Mathematical Surveys and Monographs.

[4]  Chih-Peng Li,et al.  Gaussian Integer Sequences With Ideal Periodic Autocorrelation Functions , 2012, IEEE Trans. Signal Process..

[5]  Arnaldo Spalvieri,et al.  Synchronous CDMA Based on the Cyclical Translations of a CAZAC Sequence , 2005, 2005 2nd International Symposium on Wireless Communication Systems.

[6]  E. T..  An Introduction to the Theory of Numbers , 1946, Nature.

[7]  Qiaoyan Wen,et al.  New Perfect Gaussian Integer Sequences of Period pq , 2013, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[8]  Soo-Chang Pei,et al.  Closed-Form Orthogonal DFT Eigenvectors Generated by Complete Generalized Legendre Sequence , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Zhengchun Zhou,et al.  Perfect Gaussian Integer Sequences of Odd Prime Length , 2012, IEEE Signal Processing Letters.

[10]  M. Rangaswamy,et al.  Phase-Coded Waveforms and Their Design , 2009, IEEE Signal Processing Magazine.

[11]  Irving John Good,et al.  The Interaction Algorithm and Practical Fourier Analysis , 1958 .

[12]  Ahmed H. Tewfik,et al.  Perfectly balanced binary sequences with optimal autocorrelation , 2007, 2007 14th IEEE International Conference on Electronics, Circuits and Systems.

[13]  A. Meyer,et al.  Introduction to Number Theory , 2005 .

[14]  Don Torrieri,et al.  Principles of Spread-Spectrum Communication Systems , 2004 .

[15]  Albert C. Claus,et al.  Number Theory in Science and Communications , 1998 .