# New Matrices with Good Auto and Cross-Correlation

@article{Tirkel2006NewMW, title={New Matrices with Good Auto and Cross-Correlation}, author={Andrew Z. Tirkel and Thomas E. Hall}, journal={IEICE Trans. Fundam. Electron. Commun. Comput. Sci.}, year={2006}, volume={89-A}, pages={2315-2321} }

Large sets of matrices with good auto and cross-correlation 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. These matrices can be applied to digital watermarking of images.

## 13 Citations

### 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.

### 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.

### Arrays composed from the extended rational cycle

- Computer ScienceAdv. Math. Commun.
- 2017

A unified method of obtaining multivariate recursion polynomials and their footprints for all finite multidimensional arrays and shows that the size of the footprint is invariant under dimensional transformations based on the Chinese Remainder Theorem.

### New families of asymptotically optimal doubly periodic arrays with ideal correlation constraints

- Computer ScienceCryptography and Communications
- 2015

These new families possess the same properties that make the Moreno-Maric construction suitable for communications systems and digital watermarking, size (q+1)×( q+1), weight ω=q-1, family size q−2, and correlation 2, where q is a power of a prime.

### Multidimensional linear complexity analysis of periodic arrays

- Computer ScienceApplicable Algebra in Engineering, Communication and Computing
- 2019

This paper uses Gröbner bases to develop a theory for analyzing the multidimensional linear complexity of general periodic arrays and analyzes arrays constructed using the method of composition to establish tight bounds for their multiddimensional linear complexity.

### 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…

### Group permutable constant weight codes

- Computer Science2010 IEEE Information Theory Workshop
- 2010

This work presents improvements to the Johnson Bound to bound the cardinality of the families of double-periodic arrays whose row and column length are not relatively prime and presents some families of group permutable constant weight codes and proves the optimality of these families.

### Collusion resistant fingerprinting of digital audio

- Computer ScienceSIN '11
- 2011

These fingerprints are resistant to an averaging collusion attack by hundreds or thousands of colluders, and can withstand a worst case RandNeg attack by up to 30 colluders.

### New asymptotically optimal three-dimensional wave-length/space/time optical orthogonal codes for OCDMA systems

- PhysicsCryptography and Communications
- 2020

New families of three-dimensional (3-D) optical orthogonal codes for applications to optical code-division multiple access (OCDMA) networks are presented, based in the extended rational cycle used for the 2-D Moreno-Maric construction.

### New Optimal Low Correlation Sequences for Wireless Communications

- BusinessSETA
- 2012

Three new sets of frequency hopping sequences are presented, which are converted into sequences for CDMA, and one of the CDMA sequence families is optimal with respect to the Welch bound, and two are nearly optimal.

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