Abstract
For any even integer n, the binary Kerdock sequences of period 2(2n − 1) are optimal with respect to the well-known Welch bound. Until now the correlation distribution of this family has not been known. In this paper we completely determine its correlation distribution using connections between the correlation properties of binary sequences and quaternary sequences under the Gray map.
This work of Xiaohu Tang was supported Humboldt Research Fellowship 2007, and the Teacher Research Projects of Southwest Jiaotong University. The research of T. Helleseth and A. Johansen was supported by the Norwegian Research Council.
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
Boztas, S., Hammons, R., Kumar, P.V.: 4-phase sequences with near-optimum correlation properties. IEEE Trans. Inform. Theory 38, 1101–1113 (1992)
Fan, P.Z., Darnell, M.: Sequence Design for Communications Applications. John Wiley, Chichester (1996)
Hammons, R., Kumar, P.V., Calderbank, A.N., Sloane, N.J.A., Solé, P.: The Z 4- Linearity of Kerdock, Preparata, Goethals and Related Codes. IEEE Trans. Inform. Theory 40, 301–319 (1994)
Helleseth, T., Kumar, P.V.: Sequences with low correlation. In: Pless, V., Huffman, C. (eds.) Handbook of Coding Theory, Elsevier, Amsterdam (1998)
Johansen, A., Helleseth, T., Tang, X.H.: The correlation distribution of sequences of period 2(2n − 1). IEEE Trans. Inform. Theory (to appear)
Nechaev, A.A.: Kerdock code in a cyclic form. Discrete Mathematics Appl. 1, 365–384 (1991)
Udaya, P., Siddiqi, M.U.: Optimal biphase sequences with large linear complexity derived from sequences over Z4. IEEE Trans. Inform. Theory 42, 206–216 (1996)
Tang, X.H., Udaya, P., Fan, P.Z.: Generalized binary Udaya-Siddiqi sequences. IEEE Transactions on Information Theory 53, 1225–1230 (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tang, X., Helleseth, T., Johansen, A. (2008). On the Correlation Distribution of Kerdock Sequences. 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_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-85912-3_11
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)