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A New Family of Quadriphase Sequences with Low Correlation

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Book cover Coding and Cryptology (IWCC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6639))

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Abstract

For a positive integer n, a family of quadriphase sequences with period \(4\left(2^n-1\right)\) is proposed. The correlation values of the family and their distribution are completely determined. The maximum nontrivial correlation magnitude is \(4+2^{\frac{n+3}{2}}\) for odd n.

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References

  1. Boztas, S., Hammons, R., Kumar, P.V.: 4-phase sequences with near-optimum correlation properties. IEEE Trans. Inf. Theory 38, 1103–1113 (1992)

    Article  MATH  Google Scholar 

  2. Brown, E.H.: Generalizations of the Kervaire invariant. Ann. Math. 95, 368–383 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  3. Gold, R.: Maximal recursive sequences with 3-valued cross-correlation functions. IEEE Trans. Inf. Theory 14, 154–156 (1968)

    Article  MATH  Google Scholar 

  4. 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. Algebra Eng. Commun. Comput. 19, 429–439 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Jiang, W.F., Hu, L., Tang, X.H., Zeng, X.Y.: New optimal quadriphase sequences with larger linear span. IEEE Trans. Inf. Theory 55, 458–470 (2009)

    Article  MathSciNet  Google Scholar 

  6. Kasami, T.: Weight distributions of Bose-Chaudhuri-Hocquenghem codes. In: Bose, R.C., Dowling, T.A. (eds.) Combinatorial Mathematics and Its Applications, pp. 335–357. Univ. North Carolina Press, NC (1969)

    Google Scholar 

  7. Kumar, P.V., Helleseth, T., Calderbank, A.R., Hammons Jr., A.R.: Large families of quaternary sequences with low correlation. IEEE Trans. Inf. Theory 42, 579–592 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Li, N., Tang, X.H., Zeng, X.Y., Hu, L.: On the correlation distributions of optimal quaternary sequence family \(\mathcal{U}\) and optimal binary sequence family \(\mathcal{V}\). IEEE Trans. Inf. Theory (to appear)

    Google Scholar 

  9. MacDonald, B.R.: Finite Rings with Identity. Marcel Dekker, Inc., New York (1974)

    Google Scholar 

  10. Schmidt, K.-U.: Z 4-valued quadratic forms and quaternary sequences families. IEEE Trans. Inf. Theory 42, 579–592 (1996)

    Article  MathSciNet  Google Scholar 

  11. Sidelnikov, V.M.: On mutual correlation of sequences. Soviet Math. Dokl 12, 197–201 (1971)

    Google Scholar 

  12. Solé, P.: A quaternary cyclic code, and a familly of quadriphase sequences with low correlation properties. In: Wolfmann, J., Cohen, G. (eds.) Coding Theory 1988. LNCS, vol. 388, pp. 193–201. Springer, Heidelberg (1989)

    Google Scholar 

  13. Tang, X.H., Udaya, P.: A note on the optimal quadriphase sequences families. IEEE Trans. Inform. Theory 53, 433–436 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Udaya, P., Siddiqi, M.U.: Optimal and suboptimal quadriphase sequences derived from maximal length sequences over Z 4. Appl. Algebra Eng. Commun. Comput. 9, 161–191 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  15. Welch, L.R.: Lower bounds on the maximum crosscorrelation on the signals. IEEE Trans. Inf. Theory 20, 397–399 (1974)

    Article  MATH  Google Scholar 

  16. Zeng, X.Y., Liu, J.Q., Hu, L.: Generalized Kasami sequences: the large set. IEEE Trans. Inf. Theory 53, 2587–2598 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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Li, J., Zeng, X., Hu, L. (2011). A New Family of Quadriphase Sequences with Low Correlation. In: Chee, Y.M., et al. Coding and Cryptology. IWCC 2011. Lecture Notes in Computer Science, vol 6639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20901-7_16

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  • DOI: https://doi.org/10.1007/978-3-642-20901-7_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20900-0

  • Online ISBN: 978-3-642-20901-7

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