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}
}
  • A. TirkelT. Hall
  • Published 2 August 2005
  • Computer Science
  • Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.
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… 

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References

SHOWING 1-10 OF 13 REFERENCES

New Sets of Binary and Ternary Sequences with Low Correlation

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

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

  • A. TirkelT. HallC. F. Osborne
  • Mathematics
    1988 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.

Cross-correlation properties of algebraically constructed Costas arrays

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

  • S. MaricO. Moreno
  • Computer Science
    1988 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

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

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

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.