Abstract
Galois ring m −sequences were introduced in the late 1980s and early 1990s, and have near-optimal full periodic correlations. They are related to Z 4-linear codes, and are used in CDMA communications. We consider periodic correlation and obtain algebraic expressions of the first two partial period correlation moments of the sequences belonging to families A, B and C. These correlation moments have applications in synchronisation performance of CDMA systems using Galois ring sequences. The use of Association Schemes provides us with a new uniform technique for analyzing the sequence families A, B and C.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Boztaş, S., Hammons, A.R., Vijay Kumar, P.: 4-phase sequences with near-optimum correlation properties. IEEE Trans. Inform. Theory 38(3), 1101–1113 (1992)
Boztaş, S., Udaya, P.: Partial Correlations of Galois Ring Sequences. In: Proceedings of IEEE IWSDA Workshop, Chengdu, China, 23-27 September, pp. 157–161 (2007)
Golomb, S.W., Gong, G.: Signal Design for Good Correlation. Cambridge University Press, Cambridge (2005)
Helleseth, T., Vijay Kumar, P.: Sequences with low correlation. In: Pless, V., Huffman, W.C. (eds.) Handbook of Coding Theory, vol. II, Elsevier, Amsterdam (1998)
Vijay Kumar, P., Helleseth, T., Calderbank, A.R., Hammons Jr., A.R.: Large families of quaternary sequences with low correlation. IEEE Trans. Inform. Theory 42(2), 579–592 (1996)
Solé, P.: A quaternary cyclic code, and a family of quadriphase sequences with low correlation properties. In: Cohen, G., Wolfmann, J. (eds.) Proceedings of Coding Theory and Applications. LNCS, vol. 388, pp. 193–201. Springer, Heidelberg (1989)
Sidelnikov, V.M.: On mutual correlation of sequences. Probl. Kybern. 24, 537–545 (1978)
Simon, M.K., Omura, J.K., Scholtz, R.A., Levitt, B.K.: Spread Spectrum Communications Handbook (revised ed.). McGraw Hill, New York (1994)
Tang, X.H., Udaya, P.: A Note on the Optimal Quadriphase Sequence Families. IEEE Trans. Inform. Theory 53(1), 433–436 (2007)
Udaya, P., Siddiqi, M.U.: Optimal and suboptimal quadriphase sequences derived from maximal length sequences over ℤ4. J. Appl. Algebra Eng., Commun. 9, 161–191 (1998)
Udaya, P., Boztaş, S.: On the aperiodic correlation function of Galois ring m-Sequences. In: Bozta, S., Sphparlinski, I. (eds.) AAECC 2001. LNCS, vol. 2227, pp. 229–238. Springer, Heidelberg (2001)
Welch, L.R.: Lower bounds on the maximum cross correlation of signals. IEEE Trans. Inform. Theory 20(2), 397–399 (1974)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Udaya, P., Boztaş, S. (2008). On Partial Correlations of Various Z 4 Sequence Families. In: Golomb, S.W., Parker, M.G., Pott, A., Winterhof, A. (eds) Sequences and Their Applications - SETA 2008. SETA 2008. Lecture Notes in Computer Science, vol 5203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85912-3_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-85912-3_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85911-6
Online ISBN: 978-3-540-85912-3
eBook Packages: Computer ScienceComputer Science (R0)