Constructions of families with unequal autoand cross-correlation constraints

Yang and Fuja [1] presented constructions of codes with unequal correlation constraints (λ<inf>c</inf> ≪ λ<inf>a</inf>). And specifically they have constructions for the case where λ<inf>a</inf> = 2 ≫ λ<inf>c</inf> = 1. In their work they argue that it is important to make the cross-correlation (λ<inf>c</inf>) as small as possible, and not necessarily λ<inf>a</inf> = λ<inf>c</inf>. In this work we present a method to generate new Yang-Fuja type families with correlation constraints where λ<inf>c</inf> ≪ λ<inf>a</inf>.

[1]  C. Colbourn,et al.  Recursive constructions for cyclic block designs , 1984 .

[2]  Ingemar J. Cox,et al.  Secure spread spectrum watermarking for multimedia , 1997, IEEE Trans. Image Process..

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

[4]  László Györfi,et al.  Constructions of binary constant-weight cyclic codes and cyclically permutable codes , 1992, IEEE Trans. Inf. Theory.

[6]  C. F. Osborne,et al.  A digital watermark , 1994, Proceedings of 1st International Conference on Image Processing.

[7]  A.Z. Tirkel,et al.  Image watermarking-a spread spectrum application , 1996, Proceedings of ISSSTA'95 International Symposium on Spread Spectrum Techniques and Applications.

[8]  O. Moreno,et al.  A New Construction of Multiple Target Sonar and Extended Costas Arrays with Perfect Correlation , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

[9]  Ingemar J. Cox,et al.  Secure spread spectrum watermarking for images, audio and video , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[10]  C. Colbourn,et al.  The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.

[11]  Zhen Zhang,et al.  New constructions of optimal cyclically permutable constant weight codes , 1995, IEEE Trans. Inf. Theory.

[12]  Oscar Moreno,et al.  Double Periodic Arrays with Optimal Correlation for Applications in Watermarking , 2007, SSC.

[13]  Andrew Z. Tirkel,et al.  New Matrices with Good Auto and Cross-Correlation , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[14]  Solomon W. Golomb,et al.  Two-dimensional synchronization patterns for minimum ambiguity , 1982, IEEE Trans. Inf. Theory.

[15]  Guu-chang Yang,et al.  Optical orthogonal codes with unequal auto- and cross-correlation constraints , 1995, IEEE Trans. Inf. Theory.

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

[17]  Andrew Z. Tirkel,et al.  TOWARDS A ROBUST DIGITAL WATERMARK , 1995 .

[18]  Andrew Z. Tirkel,et al.  A TWO-DIMENSIONAL DIGITAL WATERMARK , 1995 .