Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T20:18:43.603Z Has data issue: false hasContentIssue false
  • English
  • Français

Families of Generalized Weighing Matrices

Published online by Cambridge University Press:  20 November 2018

Gerald Berman
Gerald Berman*
Affiliation:
University of Waterloo, Waterloo, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Generalized weighing (GW) matrices are orthogonal matrices whose nonzero entries are roots of unity. Several families are constructed with the aid of finite geometries which include as special cases interesting examples of conference matrices and weighing matrices.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 5 , 01 October 1978 , pp. 1016 - 1028
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Berlekamp, E. R., Algebraic coding theory (McGraw Hill, New York, 1968).Google Scholar
2. Gerald, Berman, Weighing matrices and group divisible designs determined by EG(t, pn), t > 2, Utilitas Mathematica 12 (1977), 183–191.+2,+Utilitas+Mathematica+12+(1977),+183–191.>Google Scholar
3. Familites of skew circulant weighing matrices, Ars Combinatoria 4 (1977), 293–307.Google Scholar
4. Butson, A. T., Generalized Hadamard matrices, Proc. Amer. Math. Soc. 13 (1962), 894–898.Google Scholar
5. Butson, A. T., Relations among generalized Hadamard matrices, relative difference sets and maximal length recurring sequences, Can. J. Math. 15 (1963), 42–48.Google Scholar
6. Delsarte, P. and Goethals, J. M., Tri-weight codes and generalized Hadamard matrices, Information and Control 15 (1969), 192–206.Google Scholar
7. Delsarte, P., Goethals, J. M. and Seidel, J. J., Orthogonal matrices with zero diagonal, II, Can. J. Math. 23 (1971), 816–832.Google Scholar
8. Goethals, J. M. and Seidel, J. J., Orthogonal matrices with zero diagonal, Can. J. Math. 19 (1967), 1001–1010.Google Scholar
9. Mullin, R. C., A note on balanced weighing matrices, Proc. Third Australian Conference on Combinatorial Mathematics, Brisbane, Australia, 1974.Google Scholar
10. Mullin, R. C. and Stanton, R. G., Group matrices and balanced weighing designs, Utilitas Mathematica 8 (1975), 277–301.Google Scholar
11. Paley, R. E. A., On orthogonal matrices, Math, J., and Physics 12 (1933), 311–320.Google Scholar
12. Pless, V., Symmetry codes over G F‘(3) and new jive designs, J. Comb. Theory 12 (1972), 119–142.Google Scholar
13. Rao, C. R., Cyclical generation of linear subspaces of finite geometries, Proc. Conf. on Combinatorial Mathematics and its Applications, 1967, University of North Carolina, Chapel Hill (1969), 515–535.Google Scholar
14. Singer, J., A theorem on finite projective geometry and some applications to number theory, Trans. Amer. Math. Soc. 43 (1938), 377–385.Google Scholar
15. Shrikhande, S. S., Generalized Hadamard matrices and orthogonal arrays of strength two, Can. J. Math. 16 (1964), 736–740.Google Scholar
16. Vanstone, G. A. and Mullin, R. C., A note on the existence of weighing matrices ﹜Y(2în∼j, 2n) and associated combinatorial designs, Utilitas Mathematica 8 (1975), 371–381.Google Scholar
17. Yates, F., Complex experiments, J. Roy. Soc. Stat. B2 (1935), 181–223.Google Scholar