# Matrix construction using cyclic shifts of a column

@article{Tirkel2005MatrixCU, title={Matrix construction using cyclic shifts of a column}, author={Andrew Z. Tirkel and Thomas E. Hall}, journal={Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.}, year={2005}, pages={2050-2054} }

This paper describes the synthesis of matrices with good correlation, from cyclic shifts of pseudonoise columns. Optimum matrices result whenever the shift sequence satisfies the constant difference property. Known shift sequences with the constant (or almost constant) difference property are: quadratic (polynomial) and reciprocal shift modulo prime, exponential shift, Legendre shift, Zech logarithm shift, and the shift sequences of some m-arrays. We use these shift sequences to produce arrays…

## 15 Citations

### Families of 3D Arrays for Video Watermarking

- Computer ScienceSETA
- 2014

New constructions of families of binary and ternary arrays with low off-peak (periodic) autocorrelation and low cross-correlation for application to video watermarking are presented.

### Double Periodic Arrays with Good Correlation for Applications in Watermarking

- Computer Science2007 3rd International Workshop on Signal Design and Its Applications in Communications
- 2007

This paper presents a method that increases the number of sequences, and another that increasesThe number of ones keeping the correlation good and double-periodic, and combines both methods producing families of double- periodic arrays with good correlation and many dots.

### New families of arrays in two dimensions for watermarking applications

- Computer Science
- 2010

A new construction of arrays for watermarking is presented, composed from cyclic shifts of a binary column with good autocorrelation that yields a large family of binary arrays with low off-peak autOCorrelation and low cross-correlation in many new and desirable sizes.

### Double Periodic Arrays with Optimal Correlation for Applications in Watermarking

- Computer ScienceSSC
- 2007

This paper presents a method that increases the number of sequences, and another that increasesThe number of ones keeping the correlation good and double-periodic, and obtain two new constructions of Optical Orthogonal Codes.

### Recursive constructions of arrays with low autocorrelation

- Computer Science, Mathematics
- 2015

This thesis presents some of those recursive constructions of perfect and what they call "almost perfect" arrays over the quaternary (4th roots of unity) alphabet in the language of arrays, with no recourse to polynomials.

### A new method to construct double periodic arrays with optimal correlation

- Mathematics2009 IEEE Information Theory Workshop
- 2009

Double-periodic arrays with good correlation are useful for applications in multiple target Costas and sonar, optical communications, and more recently digital watermarking. There are only a few…

### Multi-dimensional arrays for watermarking

- Computer Science2011 IEEE International Symposium on Information Theory Proceedings
- 2011

This paper presents two new classes of families of multi-periodic arrays suitable for digital watermarking, large and all arrays have good auto and cross-correlation, and are available in many sizes.

### New Matrices with Good Auto and Cross-Correlation

- Computer ScienceIEICE Trans. Fundam. Electron. Commun. Comput. Sci.
- 2006

Two methods of extending family size by column multiplication and a method of extending physical size by interlacing are presented, which can be applied to digital watermarking of images.

### k-Error linear complexity for multidimensional arrays

- Computer ScienceArXiv
- 2018

This paper makes computations for some typical families of multidimensional arrays to confirm that they have a large $k$-error linear complexity for small $k$.

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

- Computer Science2010 Fourth International Conference on Network and System Security
- 2010

New families of two and three-dimensional arrays designed for watermarking, based on finite fields, have applications in surveillance, sub-image object tracking and as fingerprints for proof of tampering, audit trail monitoring and traitor tracing.

## References

SHOWING 1-10 OF 13 REFERENCES

### New Sets of Binary and Ternary Sequences with Low Correlation

- Computer ScienceSETA
- 2004

New binary and ternary sequences with low correlation and simple implementation are presented, whose columns are cyclic shifts of a short sequence or constant columns and whose shift sequence (sequence of column shifts) has the distinct difference property.

### Families of Matrices with Good Auto and Cross-Correlation

- MathematicsArs Comb.
- 2001

A family of p-1 square p% p matrices whose periodic cross-correlation values are uniformly –p,0,+p is constructed, which has resulted in the superimposed embedding of twelve of the matrices in the standard image “Lenna” and their subs equent retrieval without recourse to the unmarked image.

### A new class of spreading sequences

- Mathematics1988 IEEE 5th International Symposium on Spread Spectrum Techniques and Applications - Proceedings. Spread Technology to Africa (Cat. No.98TH8333)
- 1998

The resulting sequences form a family comparable in size and figure of merit to that of Gold codes, but available in many different (composite) lengths, and possess enhanced immunity against cryptographic attack, owing to their large linear and nonlinear span.

### Crosscorrelation of M-sequences and GMW-sequences with the same primitive polynomial

- Computer ScienceDiscret. Appl. Math.
- 1985

### Cross-correlation properties of algebraically constructed Costas arrays

- Mathematics
- 1991

The problem of determining the cross-correlation properties of signals based on algebraically constructed Costas arrays is addressed by examining the discrete cross-correlation of the algebraically…

### The role of frequency hopping in today's digital communications

- Computer Science1988 IEEE 5th International Symposium on Spread Spectrum Techniques and Applications - Proceedings. Spread Technology to Africa (Cat. No.98TH8333)
- 1998

An algebraic construction of a new family of FH codes is given based on the property of cyclic groups in finite fields; it is shown that for each field GF(p/sup m/) there exists a large number of codes of length p/Sup m/.

### Information Hiding: Techniques for Steganography and Digital Watermarking

- Computer Science
- 2000

This first comprehensive survey of steganography and watermarking and their application to modern communications and multimedia is presented.

### Information Hiding Techniques for Steganography and Digital Watermaking

- Computer Science
- 1999

This first comprehensive survey of steganography and watermarking and their application to modern communications and multimedia and an overview of "steganalysis," methods which can be used to break steganographic communication are discussed.

### Signal Design for Ultra-wideband Radio

- BusinessSETA
- 2001

A variety of sequence design problems, motivated by UWB system constraints, will be presented, and design for time-hopping, for spectral flatness, for rapid acquisition, and for multiple access will be discussed.