Families of Generalized Weighing Matrices
Canadian journal of mathematics, Tome 30 (1978) no. 5, pp. 1016-1028

Voir la notice de l'article provenant de la source Cambridge University Press

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.
Berman, Gerald. Families of Generalized Weighing Matrices. Canadian journal of mathematics, Tome 30 (1978) no. 5, pp. 1016-1028. doi: 10.4153/CJM-1978-086-8
@article{10_4153_CJM_1978_086_8,
     author = {Berman, Gerald},
     title = {Families of {Generalized} {Weighing} {Matrices}},
     journal = {Canadian journal of mathematics},
     pages = {1016--1028},
     year = {1978},
     volume = {30},
     number = {5},
     doi = {10.4153/CJM-1978-086-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-086-8/}
}
TY  - JOUR
AU  - Berman, Gerald
TI  - Families of Generalized Weighing Matrices
JO  - Canadian journal of mathematics
PY  - 1978
SP  - 1016
EP  - 1028
VL  - 30
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-086-8/
DO  - 10.4153/CJM-1978-086-8
ID  - 10_4153_CJM_1978_086_8
ER  - 
%0 Journal Article
%A Berman, Gerald
%T Families of Generalized Weighing Matrices
%J Canadian journal of mathematics
%D 1978
%P 1016-1028
%V 30
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-086-8/
%R 10.4153/CJM-1978-086-8
%F 10_4153_CJM_1978_086_8

[1] 1. Berlekamp, E. R., Algebraic coding theory (McGraw Hill, New York, 1968). Google Scholar

[2] 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] 3. Familites of skew circulant weighing matrices, Ars Combinatoria 4 (1977), 293–307. Google Scholar

[4] 4. Butson, A. T., Generalized Hadamard matrices, Proc. Amer. Math. Soc. 13 (1962), 894–898. Google Scholar

[5] 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] 6. Delsarte, P. and Goethals, J. M., Tri-weight codes and generalized Hadamard matrices, Information and Control 15 (1969), 192–206. Google Scholar

[7] 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] 8. Goethals, J. M. and Seidel, J. J., Orthogonal matrices with zero diagonal, Can. J. Math. 19 (1967), 1001–1010. Google Scholar

[9] 9. Mullin, R. C., A note on balanced weighing matrices, Proc. Third Australian Conference on Combinatorial Mathematics, Brisbane, Australia, 1974. Google Scholar

[10] 10. Mullin, R. C. and Stanton, R. G., Group matrices and balanced weighing designs, Utilitas Mathematica 8 (1975), 277–301. Google Scholar

[11] 11. Paley, R. E. A., On orthogonal matrices, Math, J., and Physics 12 (1933), 311–320. Google Scholar

[12] 12. Pless, V., Symmetry codes over G F‘(3) and new jive designs, J. Comb. Theory 12 (1972), 119–142. Google Scholar

[13] 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] 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] 15. Shrikhande, S. S., Generalized Hadamard matrices and orthogonal arrays of strength two, Can. J. Math. 16 (1964), 736–740. Google Scholar

[16] 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] 17. Yates, F., Complex experiments, J. Roy. Soc. Stat. B2 (1935), 181–223. Google Scholar

Cité par Sources :