Abstract
In this paper, a new family of quadriphase sequences with period 4(2n − 1) is proposed for n = me, where m is an odd integer. The correlation values of the family, their distribution, and the linear spans of the proposed sequences are completely determined under two situations.
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Boztas S., Hammons R., Kumar P.V.: 4-phase sequences with near-optimum correlation properties. IEEE Trans. Inf. Theory 38(3), 1103–1113 (1992)
Boztas S., Kumar P.V.: Binary sequences with Gold-like correlation but larger linear span. IEEE Trans. Inf. Theory 40(2), 532–537 (1994)
Brown E.H.: Generalizations of the Kervaire invariant. Ann. Math. 95(2), 368–383 (1972)
Gold R.: Maximal recursive sequences with 3-valued cross-correlation functions. IEEE Trans. Inf. Theory 14(1), 154–156 (1968)
Golomb S.W., Gong G.: Signal Design for Good Correlation—for Wireless Communication, Cryptography and Radar. Cambridge University Press, Cambridge (2005)
Helleseth T., Kumar P.V.: Sequences with low correlation. In: Pless, V., Huffman, C. (eds) Handbook of Coding Theory, Elsevier, Amsterdam (1998)
Jiang W.F., Hu L., Tang X.H., Zeng X.Y.: New family of binary sequences of period 4(2n − 1) with low correlation. Appl. Algebr. Eng. Commun. Comput. 19(5), 429–439 (2008)
Jiang W.F., Hu L., Tang X.H., Zeng X.Y.: New optimal quadriphase sequences with larger linear span. IEEE Trans. Inf. Theory 55(1), 458–470 (2009)
Kasami T.: Weight distribution of Bose-Chaudhuri-Hocquenghem codes. In: Bose, R.C., Dowling T.A., ((eds) Combinatorial Mathematics and Its Applications, pp. 335–357. University of North Carolina Press, Chapel Hill (1969)
Li N., Tang X.H., Zeng X.Y., Hu L.: On the correlation distributions of the optimal quaternary sequence family \({\mathcal{U}}\) and the optimal binary sequence family \({\mathcal{V}}\) . IEEE Trans. Inf. Theory 57(6), 3815–3824 (2011)
Li J., Zeng X.Y., Hu L.: A new family of quadriphase sequences with low correlation. In: Lecture Notes in Computer Science, vol. 6639, pp. 246–262 (2011).
Sarwate D.V., Pursley M.B.: Crosscorrelation properties of pseudorandom and related sequences. Proc. IEEE 68, 593–619 (1980)
Schmidt K.-U.: \({\mathbf{Z}_4}\) -valued quadratic forms and quaternary sequences families. IEEE Trans. Inf. Theory 42(2), 579–592 (2009)
Solé P.: A quaternary cyclic code, and a family of quadriphase sequences with low correlation properties. In: Lecture Notes in Computer Science, vol. 388, pp. 193–201 (1989).
Tang X.H., Udaya P., Fan P.Z.: Quadriphase sequences obtained from binary quadratic form sequences. In: Lecture Notes in Computer Science vol. 3486, pp. 243–254 (2005).
Tang X.H., Udaya P.: A note on the optimal quadriphase sequences families. IEEE Trans. Inform. Theory 53(1), 433–436 (2007)
Tang X.H., Helleseth T., Fan P.Z.: A new optimal quaternary sequence family of length 2(2n − 1) obtained from the orthogonal transformation of families \({\mathcal{B}}\) and \({\mathcal{C}}\) . Des. Codes Cryptogr. 53(3), 137–148 (2009)
Udaya P., Siddiqi M.U.: Optimal and suboptimal quadriphase sequences derived from maximal length sequences over \({\mathbf{Z}_4}\) . Appl. Algebr. Eng. Commun. Comput. 9(2), 161–191 (1998)
Zeng X.Y., Liu J.Q., Hu L.: Generalized Kasami sequences: the large set. IEEE Trans. Inf. Theory 53(7), 2587–2598 (2007)
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Li, J., Zeng, X., Tang, X. et al. A family of quadriphase sequences of period 4(2n − 1) with low correlation and large linear span. Des. Codes Cryptogr. 67, 19–35 (2013). https://doi.org/10.1007/s10623-011-9583-0
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DOI: https://doi.org/10.1007/s10623-011-9583-0