A class of almost r-phase sequences with ideal autocorrelation
Keywords:
Almost r-phase sequence, correlation distribution, cyclotomic class, cyclotomic number, ideal autocorrelation.Abstract
For an odd prime N 1 (mod r), (r) almost r-phase sequences of period N areconstructed based on cyclotomy, where r is a positive integer and is Euler’sfunction. The new sequences have ideal autocorrelation property. Moreover, thesealmost r-phase sequences are modified to obtain r (r) r-phase sequences withgood autocorrelation, which include known polyphase power-residue sequences,Legendre sequences (r 2) and quadriphase sequences (r 4). The autocorrelationdistribution of these r-phase sequences are determined completely.References
Chung, J.S., No, J.S. & Chung, H. (2011) A construction of a new family of M-ary sequences with low
correlation from Sidel’nikov sequences. IEEE Transactions on Information Theory, 57(4):2301-
Ciftlikli, C. & Develi, I. (2004) A plausible approach to determine most suitable spreading codes for a
direct-sequence CDMA system. Kuwait Journal of Science & Engineering, 31(2):235-259.
Cusick, T.W., Ding, C. & Renvall, A. (1998) Stream Ciphers and Number Theory. Elsevier, Amsterdam.
Dickson, L.E. (1935) Cyclotomy, higher congruences, and Waring’s problem. American Journal of
Mathematics, 57:391-424.
Ding, C. & Helleseth, T. (1998) On cyclotomic generator of order r. Information Processing Letters,
(1):21-25.
Golomb, S.W. & Gong, G. (2005) Signal Design for Good Correlation: For Wireless Communication,
Cryptography and Radar. Cambridge University Press, Cambridge.
Green, D.H. & Green, P.R. (2003) Polyphase power-residue sequences. Royal Society of London
Proceedings Series, A 459(2032):817-827.
Huang, B. & Tu, H. (2015) Strongly secure certificateless one-pass authenticated key agreement scheme.
Kuwait Journal of Science, 42(1):91-108.
Kim, Y.S., Chung, J.S., No, J.S. & Chung, H. (2005) On the autocorrelation distributions of Sidel’nikov
sequences. IEEE Transactions on Information Theory, 51(9):3303-3307.
Lüke, H.D., Schotten, H.D. & Hadinejad-Mahram, H. (2000) Generalised Sidelnikov sequences with
optimal autocorrelation properties. Electronics Letters, 36(6):525-527.
Meidl, W. (2009) Remarks on a cyclotomic sequence. Designs, Codes and Cryptography, 51(1):33-43.
Rushanan, J.J. (2006) Weil sequences: A family of binary sequences with good correlation properties.
Proceeding of IEEE International Symposium on Information Theory 2006, Seattle, USA, 1648-
Sidel’nikov, V.M. (1969) Some k-valued pseudo-random sequences and nearly equidistant codes. Problems
of Information Transmission, 5(1):12-16.
Storer, T. (1967) Cyclotomy and Difference Sets. Markham Publishing Co., Chicago.
Sze, T.W., Chanson, S., Ding, C., Helleseth, T. & Parker, M. (2003) Logarithm cartesian authentication
codes. Information and Computation, 184(1):93-108.
Tang, X. & Lindner, J. (2009) Almost quadriphase sequence with ideal autocorrelation property. IEEE
Signal Processing Letters, 16(1):38-40.
Wang, Z., Gong, G. & Yu, N.Y. (2013) New polyphase sequence families with low correlation derived
from the Weil bound of exponential sums. IEEE Transactions on Information Theory, 59(6):3990-
Yu, N.Y. & Gong, G. (2010) Multiplicative characters, the Weil bound, and polyphase sequence families
with low correlation. IEEE Transactions on Information Theory, 56(12):6376-6387.
Zeng, X., Hu, L. & Liu, Q. (2006) A novel method for constructing almost perfect polyphase sequences.
Lecture Notes in Computer Science, 3969:346-353.
Zhou, Z. & Tang, X. (2011) New nonbinary sequence families with low correlation, large size, and large
linear span. Applied Mathematics Letters, 24(7):1105-1110.