Compose Binary Matrices

Compose Binary 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 Matrices and M-Sequences (which formed a closed sets under the addition and with the corresponding null sequence formed additive groups and generated by feedback registers) 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, and the Traffic channel.
This research is useful to generate new sets of sequences (which are also with the corresponding null sequence additive groups) by compose Hadamard matrices and
M-sequences with the bigger lengths and the bigger minimum distance that assists to increase secrecy of these information and increase the possibility of correcting mistakes resulting in the channels of communication.

Keywords: hadamard matrices, Walsh Sequences, M-sequences, Additive group, Coefficient of Correlation, Orthogonal sequences.

Free Full-text PDF

How to cite this article:
Ahmad Hamza Al Cheikha. Compose Binary Matrices. American Journal of Computer Sciences and Applications, 2017; 1:10.DOI: 10.28933/ajcsa-2017-10-2601

[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] Byrnes, J.S.; Swick,(1970), Instant Walsh Functions, SIAM Review.,Vol. 12, pp.131.
[4] 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,.
[5] Djoković, D. Z. (2009),”Hadamard Matrices of Small Order and Yang Conjecture” http://arxiv .org/abs/0912.5091.
[6] Evangelaras, H.; Koukouvinos C.; Seberry J.(2003), applications of Hadamard matrices, Journal of telecommunication and information technology. Pp. 3-10
[7] Fraleigh, J. B. (1971), A First course In Abstract Algebra. Fourth printing, USA: Addison-Wesley publishing company.
[8] 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.
[9] Geramita, A.V., Seberry, J.(1979), Orthogonal Designs: Quadratic Forms and Hadamard Matrices, New York-Basel: Marcel Dekker.
[10] Hedayat, A.S., Sloane, N.J.A., Stufken, J.(1999), Orthogonal arrays theory and Applications, Springer-Verlag, New York.
[11] Hedayat, A., Wallis, W.D.(1978), Hadamard matrices and their applications. Ann. Stat. 6, 1184–1238
[12] Jong-Seon No, Solomon W. & Golomb,(1998), Binary Pseudorandom Sequences For period 2n-1 with Ideal Autocorrelation, IEEE Trans. Information Theory, Vol. 44 No 2, PP 814-817
[13] Kitis, L. “Paley’s Construction of Hadamard.
[14] Koukouvinos, C.; Kounias, S.(1998), An infinite class of Hadamard matrices. J Austral SocA 46, 384–394 18 Seberry et al.
[15] Lee, J. S., Miller. L. E. (1998 ), CDMA Systems Engineering Handbook. Boston, London: Artech House.
[16] Lidl, R.& Nidereiter, H.,(1994), Introduction to Finite Fields and Their Application, Cambridge University USA.
[17] Lidl, R.& Pilz,G., ”Applied Abstract Algebra,” Springer–VerlageNew York, 1984.
[18] Mac Williams, F. J.; Sloane, N. J. A. (2006), The theory of Error- correcting Codes, Amsterdam: North- Holland Publishing Company
[19] Seberry, J. (2004), Library of hadamard matrices, http// .au/ jennie/ hadamard.html.
[20] 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.
[21] Seberry, J.; Wysocki, B.J.; Wysocki, T.A.,(2003) Williamson-Hadamard spreading Sequences for DSCDMA applications. J.Wireless Commun. Mobile Comput, 3(5), 597–607 .
[22] Seberry, J.; JWysocki, B. ; AWysocki, T., On some applications of Hadamard matrices.
[23] 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
[24] Seberry J., Yamada M.,(1992), Hadamard matrices, sequences and designs, in Design Theory – a Collection of Surveys, D. J. Stinson and J. Dinitz, Eds. Wiley, Pp. 431–560.
[25] 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.
[26] Sloane, N.J.A.(2004), A library of Hadamard matrices, http// najs/ hadamard/.
[27] Sloane, N.J.A., (1976), An Analysis Of The Stricture and Complexity Of Nonlinear Binary Sequence Generators, IEEE Trans. Information Theory Vol. It 22 No 6,PP 732-736.
[28] Thomson W. Judson, (2013), Abstract Algebra: Theory and Applications, Free Software Foundation.
[29] Wolfram Notebook, Hadamard Matrix.
[30] 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.
[31] Yang; Samuel C., (1998), CDMA RF Engineering. Artech House, Boston London.
[32] Yarlagadda, R.K.; Hershey, J.E.:(1997), Hadamard matrix analysis and synthesis with applications to communications and signa l/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.