Generalization of Hadamard Matrices

Generalization of Hadamard Matrices

Dr. Ahmad Hamza Al Cheikha

Dep. of Mathematical Science, College of Arts-science and Education Ahlia Uni., Manama, Bahrain

American Journal of Computer Sciences and Applications

Hadamard’s matrices are used widely at the forward links of communication channels to mix the information on connecting to and at the backward links of these channels to sift through this information is transmitted to reach the receivers this information in correct form, specially in the pilot channels, the Sync channels, the traffic channel and so much applications in the fields; Modern communication and telecommunication systems, signal processing, optical multiplexing, error correction coding, and design and analysis of statistics.
This research is useful to generate new sets of orthogonal matrices by generalization Hadamard matrices,with getting bigger lengths and bigger minimum distance by using binary representation of the matrices that assists to increase secrecy of these information, increase the possibility of correcting mistakes resulting in the channels of communication, giving idea to construct new coders and decoders by mod p with more complexity for using these matrices and derivation new orthogonal codes or sequences.

Keywords: Hadamard matrix, Binary vector, Coefficient of Correlation, Walsh’s Sequences, Orthogonal sequences, Kronecker product, Code

Free Full-text PDF

How to cite this article:
Ahmad Hamza Al Cheikha, Generalization of Hadamard Matrices. American Journal of Computer Sciences and Applications, 2017; 1:9. DOI: 10.28933/ajcsa-2017-10-0801


[1] Al Cheikha, A. H. (2014), Composed Short Walsh’s Sequences, American International Journal
for Contemporary Scientific Research, 1(2), 81-88.
[2] Al Cheikha, A. H. (2005), Generation of sets of sequences isomorphic to Walsh sequences. Qatar
University Science Journal, 25, 16-30.
[3] Brouwer, A. E.; Cohen, A. M.; and Neumaier, A.(1989), “Hadamard Matrices” §1.8 in Distance Regular Graphs. New York: Springer-Verlag, pp. 19-20,.
[4] Djoković, D. Z. (2009),”Hadamard Matrices of Small Order and Yang Conjecture”
[5] Evangelaras, H.; Koukouvinos C.; Seberry J.(2003), applications of Hadamard matrices, Journal of telecommunication and information technology. Pp. 3-10
[6] Fraleigh, J. B. (1971), A First course In Abstract Algebra. Fourth printing, USA: Addison-Wesley publishing company.
[7] Geramita,A.V., Seberry, J.(1979), Orthogonal designs, quadratic forms and Hadamard Matrices, Lecture Notes in Pure and Applied Mathematics, vol.43, Marcel Dekker, NewYork and Basel.
[8] Geramita, A.V., Seberry, J.(1979), Orthogonal Designs: Quadratic Forms and Hadamard Matrices, New York-Basel: Marcel Dekker.
[9] Hedayat, A.S., Sloane, N.J.A., Stufken, J.(1999), Orthogonal arrays theory and Applications, Springer-Verlag, New York.
[10] Hedayat, A., Wallis, W.D.(1978), Hadamard matrices and their applications. Ann. Stat. 6, 1184–1238
[11] Kitis, L. “Paley’s Construction of Hadamard.
[12] Koukouvinos, C.; Kounias, S.(1998), An infinite class of Hadamard matrices. J Austral Math SocA 46, 384–394 18 Seberry et al.
[13] Lee, J. S., Miller. L. E. (1998 ), CDMA Systems Engineering Handbook. Boston, London: Artech House.
[14] Lidl, R., Niederreiter, H. (1986), Introduction to Finite Fields and Their Application. USA: Cambridge University.
[15] Mac Williams, F. J.; Sloane, N. J. A. (1978), The theory of Error- correcting Codes, Amsterdam: North- Holland Publishing Company
[16] Seberry, J. (2004), Library of hadamard matrices, http// jennie/ hadamard.html.
[17] Seberry, J., Yamada, M.,(1992), Hadamard matrices, sequences, and block designs, In: Dinitz JH, Stinson DR (eds) Contemporary design theory: a collection of surveys, JohnWiley & Sons, Inc., Pp 431–437.
[18] Seberry, J.; Wysocki, B.J.; Wysocki, T.A.,(2003) Williamson-Hadamard spreading equences for DSCDMA applications. J.Wireless Commun. Mobile Comput, 3(5), 597–607 .
[19] Seberry, J.; JWysocki, B. ; AWysocki, T., On some applications of Hadamard matrices.
[20] Seberry, J.; Wysocki, B.J.; Wysocki, T.A.; Tran, L.C.; Wang, Y.; Xia, T.; Zhao, Y., (2004), Complex orthogonal sequences from amicable Hadamard matrices, IEEE VTC’ Spring, Milan, Italy, 17-19 May 2004 – CD ROM, 2004
[21] Seberry J., Yamada M.,(1992), Hadamard matrices, sequences and designs, in Contemporary Design Theory – a Collection of Surveys, D. J. Stinson and J. Dinitz, Eds. Wiley, Pp. 431–560.
[22] Seberry J.; Wallis, (1972),Part IV of combinatorics: Room squares, sum free sets and Hadamard matrices, Lecture Notes in Mathematics, W. D. Wallis, A. Pen fold Street, and J. Seberry Wallis, Eds. Berlin- Heidelberg-New York: Springer, vol. 292.
[23] Sloane, N.J.A.(2004), A library of Hadamard matrices, http// najs/hadamard/.
[24] Wolfram Notebook, Hadamard Matrix.
[25] Wysocki, B.J.; Wysocki, T.A., (2002), Modified Walsh-Hadamard sequences for DS CDMA wireless systems. Int. J. Adapt. Control Signal Process., 16 589–602.
[26] Yang; Samuel C., (1998), CDMA RF Engineering. Artech House, Boston London.
[27] Yarlagadda, R.K.; Hershey, J.E.:(1997), Hadamard matrix analysis and synthesis with applications to communications and signal/image processing. Kluwer.

Terms of Use/Privacy Policy/ Disclaimer/ Other Policies:
You agree that by using our site, you have read, understood, and agreed to be bound by all of our terms of use/privacy policy/ disclaimer/ other policies (click here for details).

This work and its PDF file(s) are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.