Advertisement

Optimization Letters

, Volume 6, Issue 1, pp 211–217 | Cite as

New weighing matrices constructed from two circulant submatrices

  • I. S. Kotsireas
  • C. Koukouvinos
  • J. Seberry
Original Paper

Abstract

A number of new weighing matrices constructed from two circulants and via a direct sum construction are presented, thus resolving several open cases for weighing matrices as these are listed in the second edition of the Handbook of Combinatorial Designs.

Keywords

Weighing matrices Algorithm String sorting 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arasu K.T., Gulliver T.A.: Self-dual codes over \({\mathbb{F}_p}\) and weighing matrices. IEEE Trans. Inform. Theor. 47, 2051–2055 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Craigen R., Kharaghani H.: Orthogonal designs. In: Colbourn, C.J., Dinitz, J.H. (eds) Handbook of Combinatorial Designs. Discrete Mathematics and its Applications, 2 edn, pp. 280–295. Chapman & Hall/CRC, Boca Raton, FL (2007)Google Scholar
  3. 3.
    van Dam W.: Quantum algorithms for weighing matrices and quadratic residues. Algorithmica 34, 413–428 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Geramita A.V., Seberry J.: Orthogonal designs. Quadratic forms and hadamard matrices. Lecture Notes in Pure and Applied Mathematics, vol. 45. Marcel Dekker Inc., New York (1979)Google Scholar
  5. 5.
    Hotelling H.: Some improvements in weighing and other experimental techniques. Ann. Math. Stat. 16, 294–300 (1944)Google Scholar
  6. 6.
    Kotsireas I., Koukouvinos C.: New weighing matrices of order 2n and weight 2n−5. J. Comb. Math. Comb. Comput. 70, 197–205 (2009)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Kotsireas I., Koukouvinos C., Seberry J.: New weighing matrices of order 2n and weight 2n−9. J. Comb. Math. Comb. Comput. 72, 49–54 (2010)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Kotsireas I., Koukouvinos C., Seberry J.: Weighing matrices and string sorting. Ann. Comb. 13, 305–313 (2009)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Kotsireas I., Koukouvinos C., Pardalos P.: An efficient string sorting algorithm for weighing matrices of small weight. Optim. Lett. 4(1), 29–36 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Kotsireas, I., Koukouvinos, C., Pardalos, P.: A modified power spectral density test applied to weighing matrices with small weight. J. Comb. Optim. (to appear.)Google Scholar
  11. 11.
    Koukouvinos C., Seberry J.: Weighing matrices and their applications. J. Stat. Plann. Inference 62(1), 91–101 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Koukouvinos C., Seberry J.: New weighing matrices and orthogonal designs constructed using two sequences with zero autocorrelation function—a review. J. Stat. Plann. Inference 81(1), 153–182 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Raghavarao D.: Constructions and Combinatorial Problems in Design of Experiments, Wiley Series in Probability and Statistics. Wiley, New York-Sydney-London (1971)Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Physics and Computer ScienceWilfrid Laurier UniversityWaterlooCanada
  2. 2.Department of MathematicsNational Technical University of AthensZografou, AthensGreece
  3. 3.Centre for Computer and Information Security Research, School of Information Technology and Computer ScienceUniversity of WollongongWollongongAustralia

Personalised recommendations