Applications of Hadamard matrices

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DOI:

https://doi.org/10.26636/jtit.2003.2.176

Keywords:

Hadamard matrices, orthogonal sequences, CDMA spreading codes, Walsh functions, optical multiplexing

Abstract

We present a number of applications of Hadamard matrices to signal processing, optical multiplexing, error correction coding, and design and analysis of statistics.

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References

[1] W. T. Federer, A. Hedayat, E. T. Parker, B. L. Raktoe, E. Seiden, and R. J. Turyn, "Some techniques for constructing mutually orthogonal Latin squares", MRC Technical Summary Report no. 1030, Mathematics Research Centre University of Wisconsin, June 1971. (A preliminary version of this report appeared in the proceedings of the Fifteenth Conference on the Design of Experiments in Army Research Development and Testing, ARO-D Report 70-2, July 1970, The Office of Chief of Research and Development, Durham, North Carolina).
View in Google Scholar

[2] W. T. Federer, "On the existence and construction of a complete set of orthogonal F 4t;2t 2t -squares", Paper no. BU-564-M in the Biometrics Unit Mimeo Series, Department of Plant Breeding and Biometry, Cornell University, Ithica, New York, 14853, 1975.
View in Google Scholar

[3] A. V. Geramita and J. Seberry, Orthogonal Designs: Quadratic Forms and Hadamard Matrices. New York-Basel: Marcel Dekker, 1979.
View in Google Scholar

[4] J. Hadamard, "Résolution d'une question relative aux déterminants", Bull. Sci. Math., vol. 17, pp. 240-246, 1893.
View in Google Scholar

[5] A. Hedayat, "On the theory of the existence, non-existence and the construction of mutually orthogonal F-squares and latin squares". Ph.D. dissertation, Cornell University, June 1969.
View in Google Scholar

[6] A. Hedayat and E. Seiden, "F-square and orthogonal F-square design: A generalization of Latin square and orthogonal Latin squares design", Ann. Math. Stat., vol. 41, pp. 2035-2044, 1970.
View in Google Scholar

[7] C. Koukouvinos and J. Seberry, "New weighing matrices and orthogonal designs constructed using two sequences with zero autocorrelation function - a review", J. Stat. Plan. Infer., vol. 81, pp. 153-182, 1999.
View in Google Scholar

[8] J. Kiefer, "Construction and optimality of generalized Youden designs", in: Statistical Design and Linear Models, J. N. Srivastava, Ed. Amsterdam: North-Holland, 1975, pp. 333-353.
View in Google Scholar

[9] A. W. Lam and S. Tantaratana, "Theory and applications of spread spectrum systems", IEEE/EAB Self-Study Course, IEEE Inc., Piscataway, 1994.
View in Google Scholar

[10] V. I. Levenshtein, "A new lower bound on aperiodic cross-correlation of binary codes", in 4th Int. Symp. Commun. Theory & Appl., ISCTA'97, 1997, pp. 147-149.
View in Google Scholar

[11] J. P. Mandeli, "Complete sets of orthogonal F-squares". M.Sc. thesis, Cornell University, Aug. 1975.
View in Google Scholar

[12] I. Oppermann and B. S. Vucetic, "Complex spreading sequences with a wide range of correlation properties", IEEE Trans. Commun., vol. 45, pp. 365-375, 1997.
View in Google Scholar

[13] R. L. Plackett and J. P. Burman, "The design of optimum multifactorial experiments", Biometrika, vol. 33, pp. 305-325, 1946.
View in Google Scholar

[14] J. Seberry and R. Craigen, "Orthogonal designs", in Handbook of Combinatorial Designs, C. J. Colbourn and J. H. Dinitz, Eds. CRC Press, 1996, pp. 400-406.
View in Google Scholar

[15] J. Seberry, B. J. Wysocki, and T. A. Wysocki, "Golay sequences for DS CDMA applications", in Sixth Int. Symp. DSP Commun. Syst. DSPCS'02, Manly, TITR, Wollongong, Jan. 2002, pp. 103-108.
View in Google Scholar

[16] J. Seberry and M. Yamada, "Hadamard matrices, sequences and designs", in Contemporary Design Theory - a Collection of Surveys, D. J. Stinson and J. Dinitz, Eds. Wiley, 1992, pp. 431-560.
View in Google Scholar

[17] J. J. Sylvester, "Thoughts on inverse orthogonal matrices, simultaneous sign successions, and tessellated pavements in two or more colours, with applications to Newton's rule, ornamental tile-work, and the theory of numbers", Phil. Mag., vol. 34, pp. 461-475, 1967.
View in Google Scholar

[18] L. R. Welch, "Lower bounds on the maximum cross-correlation of signals", IEEE Trans. Inform. Theory, vol. 20, pp. 397-399, 1974.
View in Google Scholar

[19] J. Seberry Wallis, "Part IV of combinatorics: Room squares, sum-free sets and Hadamard matrices", Lecture Notes in Mathematics, W. D. Wallis, A. Penfold Street, and J. Seberry Wallis, Eds. Berlin-Heidelberg-New York: Springer, 1972, vol. 292.
View in Google Scholar

[20] C. F. J. Wu and M. Hamada, Experiments, Planning, Analysis, and Parameter Design Optimization. New York: Wiley, 2000.
View in Google Scholar

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Submitted

2023-04-07

Published

2003-06-30

Issue

No. 2 (2003)

Section

ARTICLES FROM THIS ISSUE

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Copyright (c) 2003 Journal of Telecommunications and Information Technology

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
H. Evangelaras, C. Koukouvios, and J. Seberry, “Applications of Hadamard matrices”, JTIT, vol. 12, no. 2, pp. 3–10, Jun. 2003, doi: 10.26636/jtit.2003.2.176.

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