Classification of affine resolvable 2-(27, 9, 4) designs
Document Type
Article
Publication Date
12-1996
Abstract
All affine resolvable designs with parameters of the design of the hyperplanes in ternary affine 3-space are enumerated. This enumeration implies the classification (up to equivalence), of all optimal equidistant ternary codes of length 13 and distance 9, as well as all complete orthogonal arrays of strength 2 with 3 symbols, 13 constraints and index 3. Up to isomorphism, there are exactly 68 such designs. The automorphism groups and the rank of the incidence matrices over GF(3) are computed. There are six designs with point-transitive automorphism groups, and one design with trivial group. The affine geometry design is the unique design with lowest 3-rank, and the only design with 2-transitive automorphism group.
Publication Title
Journal of Statistical Planning and Inference
Recommended Citation
Lam, C.,
&
Tonchev, V.
(1996).
Classification of affine resolvable 2-(27, 9, 4) designs.
Journal of Statistical Planning and Inference,
56(2), 187-202.
http://doi.org/10.1016/S0378-3758(96)00018-3
Retrieved from: https://digitalcommons.mtu.edu/math-fp/158
Publisher's Statement
Copyright © 1996 Published by Elsevier B.V. Publisher’s version of record: https://doi.org/10.1016/S0378-3758(96)00018-3