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Arrays over roots of unity with perfect autocorrelation and good ZCZ cross-correlation
1. | School of Mathematical Sciences, Building 20, Clayton Campus, Monash University, Victoria, 3800, Australia, Australia, Australia |
References:
[1] |
K. T. Arasu and W. de Launey, Two-dimensional perfect quaternary arrays, IEEE Trans. Inform. Theory, 47 (2001), 1482-1493.
doi: 10.1109/18.923729. |
[2] |
L. Bömer and M. Antweiler, Perfect n-phase sequences and arrays, IEEE J. Selected Areas Commun., 10 (1992), 782-789. |
[3] |
D. Calabro and J. K. Wolf, On the synthesis of two-dimensional arrays with desirable correlation properties, Inform. Control, 11 (1968), 537-560.
doi: 10.1016/S0019-9958(67)90755-3. |
[4] |
G. Caronni, Ermitteln unauthorisierter Verteiler von maschinenlesbaren Daten, ETH, Zurich, Switzerland, Tech. Rep., 1993. |
[5] |
W. Chi and N. George, Phase-coded aperture for optical imaging, Optics Commun., 282 (2009), 2110-2117. |
[6] |
D. C. Chu, Polyphase codes with good periodic correlation properties, IEEE trans. Inform. Theory, 18 (1972), 531-532.
doi: 10.1109/TIT.1972.1054840. |
[7] |
T. Cox and P. D'Antonio, "Acoustic Absorbers and Diffusers,'' $2^{nd}$ edition, Taylor and Francis, 2009. |
[8] |
P. Z. Fan and M.Darnell, The synthesis of perfect sequences, Lecture Notes Comp. Sci. Crypt. Coding, 1025 (1995), 63-73.
doi: 10.1007/3-540-60693-9_9. |
[9] |
E. E. Fenimore and T. M. Cannon, Coded aperture imaging with uniformly redundant arrays, Applied Optics, 17 (1978), 337-347.
doi: 10.1364/AO.17.000337. |
[10] |
R. L. Frank, S. A. Zadoff and R. Heimiller, Phase shift pulse codes with good periodic correlation properties, IRE Trans. Inform. Theory, 8 (1962), 381-382.
doi: 10.1109/TIT.1962.1057786. |
[11] |
F. Hartung and M. Kutter, Multimedia watermarking techniques, Proc. IEEE, 87 (1999), 1079-1107.
doi: 10.1109/5.771066. |
[12] |
R. C. Heimiller, Phase shift pulse codes with good periodic correlation properties, IRE Trans. Inform. Theory, 7 (1961), 254-257.
doi: 10.1109/TIT.1961.1057655. |
[13] |
V. P. Ipatov, Contribution to the theory of sequence with perfect periodic autocorrelation properties, Radio Engin. Electr. Phys., 25 (1980), 31-34. |
[14] |
J. Jedwab and C. Mitchell, Constructing new perfect binary arrays, Electronic Letters, 24 (1988), 650-652.
doi: 10.1049/el:19880440. |
[15] |
L. E. Kopilovich, On perfect binary arrays, Electronics Letters, 24 (1988), 566-567.
doi: 10.1049/el:19880385. |
[16] |
A. Koz, G. A. Triantafyllidis and A. Aydin, 3D watermarking: techniques and directions, in "Three-Dimensional Television: Capture, Transmission, and Display'' (eds. H.M. Ozaktas and L. Onural), Springer-Verlag, (2007), 427-470.
doi: 10.1007/978-3-540-72532-9_12. |
[17] |
H-D. Lüke, Sequences and arrays with perfect periodic correlation, IEEE Trans. Aerospace Electr. Sys., 24 (1988), 287-294. |
[18] |
S. L. Ma and W. S. Ng, On non-existence of perfect and nearly perfect sequences, Int. J. Inform. Coding Theory, 1 (2009), 15-38.
doi: 10.1504/IJICOT.2009.024045. |
[19] |
F. J. MacWilliams and N. J. A. Sloane, Pseudo-random sequences and arrays, Proc. IEEE, 64 (1976), 1715-1729.
doi: 10.1109/PROC.1976.10411. |
[20] |
A. Milewski, Periodic sequences with optimal properties for channel estimation and fast start-up equalization, IBM J. Res. Development, 27 (1983), 426-431.
doi: 10.1147/rd.275.0426. |
[21] |
B. G. Mobasseri, Direct sequence watermarking of digital video using m-frames, in "ICIP,'' (1998), 399-403.
doi: 10.1109/ICIP.1998.723399. |
[22] |
W. H. Mow, "A Study of Correlation of Sequences,'' Ph.D thesis, The Chinese University of Hong Kong, 1993. |
[23] |
J. Salvi, J. Pages and J. Batlle, Pattern codification strategies in structured light systems, Pattern Recognition, 37 (2004), 827-849.
doi: 10.1016/j.patcog.2003.10.002. |
[24] |
M. R Schroeder, "Number Theory in Science and Communications, with Applications to Physics, Digital Information, Computing and Self-Similarity,'' Springer, 2006. |
[25] |
K. Tanaka, Y. Nakamura and K. Matsui, Embedding secret information into a dithered multilevel image, in "Proc. IEEE Military Commun. Conf.,'' (1990), 216-220. |
[26] |
A. Z. Tirkel, C. F. Osborne and T. E. Hall, Image and watermark registration, Signal Processing J., 66 (1998), 373-383.
doi: 10.1016/S0165-1684(98)00016-4. |
[27] |
A. Z. Tirkel, G. A. Rankin, R. M. Van Schyndel, W. J. Ho, N. R. A. Mee and C. F. Osborne, Electronic watermark, in "Digital Image Comp. Tech. Appl. (DICTA’93),'' (1993), 666-673. |
[28] |
P. Wild, Infinite families of perfect binary arrays,, Electronics letters., ().
doi: 10.1049/el:19880575. |
[29] |
R. B. Wolfgang and E. J. Delp, A watermark for digital images, in "Proc. International Conference on Image Processing,'' Lausanne, Switzerland, (1996), 219-222.
doi: 10.1109/ICIP.1996.560423. |
[30] |
R. B. Wolfgang and E. J. Delp, A watermarking technique for digital imagery: Further studies, in "Proc. International Conference on Imaging Sciences, Systems and Technology,'' Las Vegas, (1997), 279-287. |
[31] |
R. B. Wolfgang and E. J. Delp, "Authentication of Signals Using Watermarks,'' U.S. Patent 6,625,295, September 2003. |
[32] |
J. Zhao and E. Koch, A generic digital watermarking model, Comp. Graphics, 22 (1998), 397-403. |
show all references
References:
[1] |
K. T. Arasu and W. de Launey, Two-dimensional perfect quaternary arrays, IEEE Trans. Inform. Theory, 47 (2001), 1482-1493.
doi: 10.1109/18.923729. |
[2] |
L. Bömer and M. Antweiler, Perfect n-phase sequences and arrays, IEEE J. Selected Areas Commun., 10 (1992), 782-789. |
[3] |
D. Calabro and J. K. Wolf, On the synthesis of two-dimensional arrays with desirable correlation properties, Inform. Control, 11 (1968), 537-560.
doi: 10.1016/S0019-9958(67)90755-3. |
[4] |
G. Caronni, Ermitteln unauthorisierter Verteiler von maschinenlesbaren Daten, ETH, Zurich, Switzerland, Tech. Rep., 1993. |
[5] |
W. Chi and N. George, Phase-coded aperture for optical imaging, Optics Commun., 282 (2009), 2110-2117. |
[6] |
D. C. Chu, Polyphase codes with good periodic correlation properties, IEEE trans. Inform. Theory, 18 (1972), 531-532.
doi: 10.1109/TIT.1972.1054840. |
[7] |
T. Cox and P. D'Antonio, "Acoustic Absorbers and Diffusers,'' $2^{nd}$ edition, Taylor and Francis, 2009. |
[8] |
P. Z. Fan and M.Darnell, The synthesis of perfect sequences, Lecture Notes Comp. Sci. Crypt. Coding, 1025 (1995), 63-73.
doi: 10.1007/3-540-60693-9_9. |
[9] |
E. E. Fenimore and T. M. Cannon, Coded aperture imaging with uniformly redundant arrays, Applied Optics, 17 (1978), 337-347.
doi: 10.1364/AO.17.000337. |
[10] |
R. L. Frank, S. A. Zadoff and R. Heimiller, Phase shift pulse codes with good periodic correlation properties, IRE Trans. Inform. Theory, 8 (1962), 381-382.
doi: 10.1109/TIT.1962.1057786. |
[11] |
F. Hartung and M. Kutter, Multimedia watermarking techniques, Proc. IEEE, 87 (1999), 1079-1107.
doi: 10.1109/5.771066. |
[12] |
R. C. Heimiller, Phase shift pulse codes with good periodic correlation properties, IRE Trans. Inform. Theory, 7 (1961), 254-257.
doi: 10.1109/TIT.1961.1057655. |
[13] |
V. P. Ipatov, Contribution to the theory of sequence with perfect periodic autocorrelation properties, Radio Engin. Electr. Phys., 25 (1980), 31-34. |
[14] |
J. Jedwab and C. Mitchell, Constructing new perfect binary arrays, Electronic Letters, 24 (1988), 650-652.
doi: 10.1049/el:19880440. |
[15] |
L. E. Kopilovich, On perfect binary arrays, Electronics Letters, 24 (1988), 566-567.
doi: 10.1049/el:19880385. |
[16] |
A. Koz, G. A. Triantafyllidis and A. Aydin, 3D watermarking: techniques and directions, in "Three-Dimensional Television: Capture, Transmission, and Display'' (eds. H.M. Ozaktas and L. Onural), Springer-Verlag, (2007), 427-470.
doi: 10.1007/978-3-540-72532-9_12. |
[17] |
H-D. Lüke, Sequences and arrays with perfect periodic correlation, IEEE Trans. Aerospace Electr. Sys., 24 (1988), 287-294. |
[18] |
S. L. Ma and W. S. Ng, On non-existence of perfect and nearly perfect sequences, Int. J. Inform. Coding Theory, 1 (2009), 15-38.
doi: 10.1504/IJICOT.2009.024045. |
[19] |
F. J. MacWilliams and N. J. A. Sloane, Pseudo-random sequences and arrays, Proc. IEEE, 64 (1976), 1715-1729.
doi: 10.1109/PROC.1976.10411. |
[20] |
A. Milewski, Periodic sequences with optimal properties for channel estimation and fast start-up equalization, IBM J. Res. Development, 27 (1983), 426-431.
doi: 10.1147/rd.275.0426. |
[21] |
B. G. Mobasseri, Direct sequence watermarking of digital video using m-frames, in "ICIP,'' (1998), 399-403.
doi: 10.1109/ICIP.1998.723399. |
[22] |
W. H. Mow, "A Study of Correlation of Sequences,'' Ph.D thesis, The Chinese University of Hong Kong, 1993. |
[23] |
J. Salvi, J. Pages and J. Batlle, Pattern codification strategies in structured light systems, Pattern Recognition, 37 (2004), 827-849.
doi: 10.1016/j.patcog.2003.10.002. |
[24] |
M. R Schroeder, "Number Theory in Science and Communications, with Applications to Physics, Digital Information, Computing and Self-Similarity,'' Springer, 2006. |
[25] |
K. Tanaka, Y. Nakamura and K. Matsui, Embedding secret information into a dithered multilevel image, in "Proc. IEEE Military Commun. Conf.,'' (1990), 216-220. |
[26] |
A. Z. Tirkel, C. F. Osborne and T. E. Hall, Image and watermark registration, Signal Processing J., 66 (1998), 373-383.
doi: 10.1016/S0165-1684(98)00016-4. |
[27] |
A. Z. Tirkel, G. A. Rankin, R. M. Van Schyndel, W. J. Ho, N. R. A. Mee and C. F. Osborne, Electronic watermark, in "Digital Image Comp. Tech. Appl. (DICTA’93),'' (1993), 666-673. |
[28] |
P. Wild, Infinite families of perfect binary arrays,, Electronics letters., ().
doi: 10.1049/el:19880575. |
[29] |
R. B. Wolfgang and E. J. Delp, A watermark for digital images, in "Proc. International Conference on Image Processing,'' Lausanne, Switzerland, (1996), 219-222.
doi: 10.1109/ICIP.1996.560423. |
[30] |
R. B. Wolfgang and E. J. Delp, A watermarking technique for digital imagery: Further studies, in "Proc. International Conference on Imaging Sciences, Systems and Technology,'' Las Vegas, (1997), 279-287. |
[31] |
R. B. Wolfgang and E. J. Delp, "Authentication of Signals Using Watermarks,'' U.S. Patent 6,625,295, September 2003. |
[32] |
J. Zhao and E. Koch, A generic digital watermarking model, Comp. Graphics, 22 (1998), 397-403. |
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