On symmetric nets and generalized Hadamard matrices from affine designs
Document Type
Article
Publication Date
3-2000
Abstract
Symmetric nets are affine resolvable designs whose duals are also affine. It is shown that. up to isomorphism, there are exactly four symmetric (3, 3)-nets (v=b=27,k=9), and exactly two inequivalent 9×9 generalized Hadamard matrices over the group of order 3. The symmetric (3, 3)-nets are found as subnets of affine resolvable 2-(27, 9, 4) designs. Ten of the 68 non-isomorphic affine resolvable 2-(27, 9, 4) designs are not extensions of symmetric (3, 3)-subnets, providing the first examples of affine 2-(q3, q2, q2−1/q−1) designs without symmetric (q, q)-subnets.
Publication Title
Journal of Geometry
Recommended Citation
Mavron, V. C.,
&
Tonchev, V.
(2000).
On symmetric nets and generalized Hadamard matrices from affine designs.
Journal of Geometry,
67(1-2), 180-187.
http://doi.org/10.1007/BF01220309
Retrieved from: https://digitalcommons.mtu.edu/math-fp/139
Publisher's Statement
© Birkhäuser Verlag 2000. Publisher’s version of record: https://doi.org/10.1007/BF01220309