Skip to main content
SpringerLink
Log in

A New Family of Amicable Hadamard Matrices

  • Published:
Journal of Statistical Theory and Practice Aims and scope Submit manuscript

Abstract

We study constructions for amicable Hadamard matrices. The family for orders 2t, t a positive integer, is explicitly exhibited. We also show that there are amicable Hadamard matrices of order (2t - 1)r + 1 for any odd integer r > 1. Now we have orders 15r + 1, 63r + 1, 255r + 1, 511r + 1, …, r > 1 an odd integer, for the first time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Adams S. S., 2009. A journey of discovery: Orthogonal matrices and communications. AMS Contemp. Math. Ser. 479, 1–9.

    Article  MathSciNet  Google Scholar 

  • Belevitch, V. 1968. Conference networks and Hadamard matrices. Ann. Soc. Sci. Brux., T82, 13–32.

    MathSciNet  MATH  Google Scholar 

  • Belevitch, V. 1950. Theory of 2n-terminal networks with applications to conference telephony, Electr. Commun., 27(3), 231–244.

    Google Scholar 

  • Delsarte, P., J. M. Goethals, and J. J. Seidel. 1971. Orthogonal matrices with zero diagonal. Can. J. Math., 23, 816–832.

    Article  MathSciNet  Google Scholar 

  • Djokovic, D. 1992. Skew Hadamard matrices of order 4 × 37 and 4 × 43. J. Combin. Theory Ser. A, 61(2), 319–321.

    Article  MathSciNet  Google Scholar 

  • Djokovic, D. 2008. Skew-Hadamard matrices of orders 188 and 388 exist. Int. Math. Forum, 3(21–24), 1063–1068.

    MathSciNet  MATH  Google Scholar 

  • Djokovic, D. 2008. Skew-Hadamard matrices of orders 436, 580, and 988 exist. J. Combin. Des. 16(6), 493–498.

    Article  MathSciNet  Google Scholar 

  • Fletcher, R. J., Koukouvinos, and J. Seberry. 2004. New skew-Hadamard matrices of order 2.59 and new D-optimal designs of order 2.59. Discrete Math., 286(3), 251–253.

    Article  MathSciNet  Google Scholar 

  • Geramita, A. V., N. J. Pullman, and J. Seberry Wallis. 1974. Families of weighing matrices. Bull. Aust. Math. Soc., 10, 119–122.

    Article  MathSciNet  Google Scholar 

  • Geramita, A. V., and J. Seberry. 1979. Orthogonal designs: Quadratic forms and Hadamard matrices. Lecture Notes in Pure and Applied Mathematics, New York, NY, Marcel Dekker.

    MATH  Google Scholar 

  • Goldberg, K. 1966. Hadamard matrices of order cube plus one. Proc. Am. Math. Soc. 17, 744–746.

    Article  MathSciNet  Google Scholar 

  • Paley, R. E. A. C. 1933. On orthogonal matrices. J. Math. Phys., 12, 311–320.

    Article  Google Scholar 

  • Seberry, J., and M. Yamada. 1992. Hadamard matrices, sequences, and block designs. In Contemporary design theory: A collection of surveys, ed. J. H. Dinitz and D. R. Stinson, 431–560. New York, NY, John Wiley and Sons.

    Google Scholar 

  • Seberry Wallis, J. 1971. Combinatorial matrices. Ph.D. Thesis, La Trobe University, Melbourne, Australia.

    Google Scholar 

  • Seberry Wallis, J. 1972. Hadamard matrices. In W. D. Wallis, Anne Penfold Street and Jennifer Seberry Wallis, Combinatorics: Room squares, sum-free sets and Hadamard matrices, ed. W. D. Wallis, A. P. Street, and J. Seberry Wallis, Lecture Notes in Mathematics, 128; 273–490. Springer Verlag, Berlin.

    MATH  Google Scholar 

  • Tarokh, V., H. Jafarkhani, and A. R. Calderbank. 1999. Space-time codes from orthogonal designs. IEEE Trans. Inform. Theory, 45, 1456–1467.

    Article  MathSciNet  Google Scholar 

  • Turyn, R. J. 1971. C-matrices of arbitrary powers. Bull. Can. Math. Soc., 23, 531–535.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Computer and Information Security Research, SCSSE, University of Wollongong, Wollongong, New South Wales, 2522, Australia

    Jennifer Seberry

Authors
  1. Jennifer Seberry
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jennifer Seberry.

Additional information

In memory of Professor J. D. Srivastava.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Seberry, J. A New Family of Amicable Hadamard Matrices. J Stat Theory Pract 7, 650–657 (2013). https://doi.org/10.1080/15598608.2013.781469

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1080/15598608.2013.781469

AMS Subject Classification

Keywords

Search

Navigation