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Two-dimensional binary arrays with good autocorrelation

Y.K. Chan, M.K. Siu, P. Tong
1979 Information and Control  
Contr. 11) investigate the autocorrelation properties of certain periodic two-dimensional arrays.  ...  This note points out a relationship between periodic p × q-arrays with two-level antocorrelation and difference sets in the group C(p) × C(q), where C(n) denote the cyclic group of order n.  ...  Calabro and Wolf (1968) investigate the autocorrelation properties of certain periodic two-dimensional arrays.  ... 
doi:10.1016/s0019-9958(79)90617-x fatcat:7remowt43jaqhb5z53ahiqwyn4

On the synthesis of two-dimensional arrays with desirable correlation properties

Domenick Calabro, Jack K. Wolf
1967 Information and Control  
This paper considers the synthesis of two-dimensional, periodic, binary and nonbinary sequences (arrays) which exhibit similar properties for their two-dimensional autocorrelation functions.  ...  A class of binary arrays is presented which are the two-dimensional analog of the quadratic residue sequences and are shown to have out-of-phase autocorrelation of --1, or to alternate between -~1 and  ...  Methods of constructing two-dimensional arrays based upon good one-dimensional sequences are also discussed.  ... 
doi:10.1016/s0019-9958(67)90755-3 fatcat:p2qnciur4bgs3cxukuxzsgfnqu

Sequences and arrays with perfect periodic correlation

H.D. Luke
1988 IEEE Transactions on Aerospace and Electronic Systems  
The construction is extended to two-dimensional perfect arrays.  ...  Properties and methods for synthesizing sequences with perfect periodic autocorrelation functions and good energy efficiency are discussed.  ...  PERFECT TWO-DIMENSIONAL ARRAYS A. Correlation Properties C.  ... 
doi:10.1109/7.192096 fatcat:qxvgxpji4fgnbay3bacfbmjbju

Code-fed omnidirectional arrays

S.E. El-Khamy, O.A. Abdel-Alim, A.M. Rushdi, A.H. Banah
1989 IEEE Journal of Oceanic Engineering  
Examples of omnidirectional linear and planar arrays fed with Barker codes, Kuttruff-Quadt trial and error two-dimensional binary codes, and nonbinary Huffman-type codes are presented.  ...  The basic theory of such code-fed arrays is reviewed and it is shown that almost omnidirectional patterns result when codes with sharp autocorrelation functions are used as the feeding sequences.  ...  Table IV shows two different combinations of Barker codes used for obtaining two-dimensional binary codes for feeding planar arrays.  ... 
doi:10.1109/48.35989 fatcat:xvlhrdwfendqhmlhbb2i24elqy

New families of arrays in two dimensions for watermarking applications

O. Moreno, A.Z. Tirkel, U. Parampalli, R.G. van Schyndel
2010 Electronics Letters  
A new construction of arrays for watermarking is presented. The arrays are composed from cyclic shifts of a binary column with good autocorrelation.  ...  This yields a large family of binary arrays with low off-peak autocorrelation and low cross-correlation in many new and desirable sizes.  ...  The essential ingredients are a column sequence with good autocorrelation, and a shift sequence which is applied as a cyclic shift to the column sequences to form a watermarking array.  ... 
doi:10.1049/el.2010.2122 fatcat:xjqcikce7zdwjc2i37b3cjv7em

Arrays over roots of unity with perfect autocorrelation and good ZCZ cross-correlation

Andrew Z. Tirkel, Thomas E. Hall, Samuel T. Blake
2013 Advances in Mathematics of Communications  
We present a new construction for two-dimensional, perfect autocorrelation arrays over roots of unity. These perfect arrays are constructed from a block of perfect column sequences.  ...  The columns are then multiplied by a perfect sequence over roots of unity, which, when folded into an array commensurate with our block width has the array orthogonality property.  ...  r distinct arrays. Each array has r 4 two-dimensional shifts, so there are at least r r 2 (r!) r r 4 arrays, no two of which are shifts of each other.  ... 
doi:10.3934/amc.2013.7.231 fatcat:cdzwozyc25hbtdugqkxcegzige

Families of Multidimensional Arrays with Good Autocorrelation and Asymptotically Optimal Cross-correlation [article]

Sam Blake
2020 arXiv   pre-print
We introduce a construction for families of 2n-dimensional arrays with asymptotically optimal pairwise cross-correlation.  ...  These arrays are constructed using a circulant array of n-dimensional Legendre arrays.  ...  The concept of binary two-dimensional doubly periodic arrays with optimal off-peak autocorrelation was introduced by Gordon in 1966 [8] . Such arrays are two-dimensional analogues of m-sequences.  ... 
arXiv:2001.08894v2 fatcat:r52ov4vpovbc7kws5jr4zphkga

Speckle interferometry with a linear digicon detector

G. D. Schmidt, J. R. P. Angel, R. Harms
1977 Publications of the Astronomical Society of the Pacific  
The extension of this method to a two-dimensional device and problems associated with speckle interferometry at very low light levels are discussed.  ...  Results are presented for observations of two binary systems and Nova Cygni 1975.  ...  Greg Schmidt for developing and coding the rapid autocorrelation algorithm.  ... 
doi:10.1086/130143 fatcat:ldtibrc5enae5borbvq4oanqje

New Matrices with Good Auto and Cross-Correlation

A. TIRKEL
2006 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
Large sets of matrices with good auto and crosscorrelation are rare.  ...  We present two such constructions, a method of extending family size by column multiplication and a method of extending physical size by interlacing.  ...  Arrays with good autocorrelation have been used in Coded Aperture Optics, Structured Light and related areas. Families of arrays with good auto and cross-correlation are rare.  ... 
doi:10.1093/ietfec/e89-a.9.2315 fatcat:bgs6i5jtl5hvlov2krkmiygzdm

Families of 3D Arrays for Video Watermarking [chapter]

Sam Blake, Oscar Moreno, Andrew Z. Tirkel
2014 Lecture Notes in Computer Science  
This paper presents new constructions of families of binary and ternary arrays with low off-peak (periodic) autocorrelation and low cross-correlation for application to video watermarking.  ...  The shift sequences are new, while the column sequence is a Sidelnikov sequence, and the column array is a multi-dimensional Legendre array.  ...  We call this new array a two-dimensional Legendre array. A two dimensional 7 × 7 Legendre array derived from Fig. 1 (a) is shown in Fig. 1(b) .  ... 
doi:10.1007/978-3-319-12325-7_12 fatcat:samavxgcdbh7ffegciuhs6i2ly

Matrix Construction Using Cyclic Shifts of a Column [article]

Andrew Z Tirkel, Tom E Hall
2005 arXiv   pre-print
This paper describes the synthesis of matrices with good correlation, from cyclic shifts of pseudonoise columns.  ...  and the shift sequences of some m-arrays.  ...  CONCLUSION This paper shows how matrices with good two dimensional autocorrelation and cross-correlation can be synthesized by using cyclic shifts of pseudonoise columns.  ... 
arXiv:cs/0508022v1 fatcat:mogdnjxxcjecto2r6jquqaxjsm

New Families of 2D & 3D Arrays for Sub-image Watermarking

Oscar Moreno, Andrew Tirkel, Ron van Schyndel, Udaya Parampalli
2010 2010 Fourth International Conference on Network and System Security  
The arrays have good auto and cross-correlation with other family members.  ...  This paper presents new families of two and threedimensional arrays designed for watermarking. The array construction is algebraic, based on finite fields.  ...  Two Dimensional Constructions The essential ingredients are a column sequence with good autocorrelation and a matrix (alternatively referred to as a shift sequence).  ... 
doi:10.1109/nss.2010.64 dblp:conf/nss/MorenoTSU10 fatcat:kgkynhpmubdylecib7jxkcqfau

New Optimal Low Correlation Sequences for Wireless Communications [chapter]

Oscar Moreno, Andrew Tirkel
2012 Lecture Notes in Computer Science  
One of the CDMA sequence families is optimal with respect to the Welch bound, and two are nearly optimal.  ...  The CDMA sequences are constructed using a composition method, which combines new shift sequences with pseudonoise columns to form an array.  ...  The CRT can also be applied to convert three dimensional arrays with a pair of relatively prime dimensions into two dimensional arrays. 3D arrays of the type p × p × p 2 − 1 described in [16] can be  ... 
doi:10.1007/978-3-642-30615-0_20 fatcat:rbktexfuhjgfdejy72nb2ylllu

New Sets of Binary and Ternary Sequences with Low Correlation [chapter]

Evgeny I. Krengel, Andrew Z. Tirkel, Tom E. Hall
2005 Lecture Notes in Computer Science  
We use this to construct new arrays which have at most one column matching for any two dimensional cyclic shift and therefore have low off-peak autocorrelation.  ...  The columns of the array can be multiplied by binary orthogonal sequences of commensurate length to produce a set of arrays with low cross-correlation.  ...  There are 2 other shifts of such a multiplication sequence, so that this method yields 4 binary arrays with good auto and cross-correlation.  ... 
doi:10.1007/11423461_15 fatcat:p5koewm6dffw5pija3nx7rtdnu

First Results from the New GSU CCD Speckle Camera

William I. Hartkopf
1986 Symposium - International astronomical union  
These new data handling techniques are outlined, with a few words about overall accuracy and a brief description of new equipment which should further improve our speckle program at GSU.  ...  microchannel plate intensifier, coupled via a fiber optic plug to a two-dimensional CCD.  ...  This corrected binary peak is finally fit by either a two-dimensional Gaussian or polynomial to determine the position of the secondary peak relative to the primary.  ... 
doi:10.1017/s0074180900076725 fatcat:wdubeicwsveg5lhzryvd2ycura
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