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New Constructions of Quaternary Hadamard Matrices

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Sequences and Their Applications - SETA 2004 (SETA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3486))

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Abstract

In this paper, we propose two new construction methods for quaternary Hadamard matrices. By the first method, which is applicable for any positive integer n, we are able to construct a quaternary Hadamard matrix of order 2n from a binary sequence with ideal autocorrelation. The second method also gives us a quaternary Hadamard matrix of order 2n from a binary extended sequence of period 2n – 1, where n is a composite number.

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References

  1. Again, S.S.: Hadamard matrices and their Applications. Lecture Notes in Mathematics, vol. 1168. Springer, New York (1980)

    Google Scholar 

  2. Boztas, S., Hammons, R., Kumar, P.V.: 4-phase sequences with near optimum correlation properties. IEEE Trans. on Inform. theory 38, 1101–1113 (1992)

    Article  MATH  Google Scholar 

  3. Craigen, R.: Hadamard matrices and designs. In: Colbourn, C.J., Dinitz, J.H. (eds.) CRC Handbook of Combinatorial Designs, ch. IV(24), pp. 370–377. CRC Press, New York (1996)

    Google Scholar 

  4. Kim, J.-H., Song, H.-Y.: Existence of cyclic Hadamard difference sets and its relation to binary sequences wiht ideal autocorrelation. J. Commun. Networks 1(1), 14–18 (1999)

    Google Scholar 

  5. Kim, S.H., Jang, J.W., No, J.S., Chung, H.: New construction of quaternary low correlation zone sequences. submitted to IEEE Trans. Inform. Theory (2004)

    Google Scholar 

  6. Kim, S.-H., Chung, H., No, J.-S., Helleseth, T.: New cyclic relative difference sets constructed from d-homogeneous functions with difference-balanced property. IEEE Trans. Inform. Theory (to appear)

    Google Scholar 

  7. Klapper, A.: d-form sequence: Families of sequences with low correlation values and large linear spans. IEEE Trans. Inform. Theory 41(2), 423–431 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. van Lint, J.H., Wilson, R.M.: A course in combinatorics. Cambridge Univ. Press, New York (1992)

    MATH  Google Scholar 

  9. Matsufuji, S., Suehiro, N.: Complex Hadamard matrices related to bent sequences. IEEE Trans. on Inform. Theory 42(2), 637 (1996)

    Article  MATH  Google Scholar 

  10. No, J.-S.: New cyclic difference sets with Singer parameters constructed from d-homogeneous functions. Designs, Codes and Cryptography 33(3), 199–213 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. No, J.-S., Yang, K., Chung, H., Song, H.-Y.: On the construction of binary sequences with ideal autocorrelation property. In: Proc. IEEE Int. Symp. Inform. Theory and Its Appl (ISITA 1996), Victoria, British Columbia, Canada, pp. 837–840 (1996)

    Google Scholar 

  12. Popovic, B.M., Suehiro, N., Fan, P.Z.: Orthogonal sets of quadriphase sequences with good correlation properties. IEEE Trans. on Inform. Theory 48(4), 956–959 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Seberry, J., Yamada, M.: Hadamard matrices, sequences, and block design. Contemporary Design Theory: Collection of Surveys, 431–569 (1992)

    Google Scholar 

  14. Simon, M.K., et al.: Spread Spectrum Communications, McGraw-Hill, vol. 1. Computer Science Press, Rockville (1994) McGraw-Hill (revised ed.)

    Google Scholar 

  15. Song, H.-Y., Golomb, S.W.: On the existence of cyclic Hadamard difference sets. IEEE Trans. Inform. Theory IT-40, 1266–1268 (1994)

    Article  Google Scholar 

  16. TIA/EIA/IS-95: Mobile Station-Base Station Compatibility Standard for Dual-Mode Wideband Spread Spectrum Cellular System. Telecommunications Industry Association as a North American 1.5 MHz Cellular CDMA Air-Interface Standard (1993)

    Google Scholar 

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Jang, JW., Kim, SH., No, JS., Chung, H. (2005). New Constructions of Quaternary Hadamard Matrices. In: Helleseth, T., Sarwate, D., Song, HY., Yang, K. (eds) Sequences and Their Applications - SETA 2004. SETA 2004. Lecture Notes in Computer Science, vol 3486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11423461_27

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  • DOI: https://doi.org/10.1007/11423461_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26084-4

  • Online ISBN: 978-3-540-32048-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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