Consider a combinatorial design D with a full automorphism group G D.
The automorphism group G of a design resolution R is a subgroup of G D.
This subgroup maps each parallel class of R into a parallel class of R.
Two resolutions R 1 and R 2 of D are isomorphic if some automorphism
from G D maps each parallel class of R 1 to a parallel class of R 2. If G D is
very big, the computation of the automorphism group of a resolution and the
check for isomorphism of two resolutions might be difficult.
Such...
Resolutions which are orthogonal to at least one other resolution (RORs) and sets of m mutually orthogonal resolutions (m-MORs) of 2-(v, k, λ) designs are considered. A dependence of the number of nonisomorphic RORs and m-MORs of multiple designs on the number of inequivalent sets of v/k − 1 mutually orthogonal latin squares (MOLS) of size m is obtained. ACM Computing Classification System (1998): G.2.1.
∗ This work was partially supported by the Bulgarian National Science Fund under...
∗ This work has been partially supported by the Bulgarian NSF under Contract No. I-506/1995.
In this note we construct five new symmetric 2-(61,16,4) designs
invariant under the dihedral group of order 10. As a by-product we
obtain 25 new residual 2-(45,12,4) designs. The automorphism groups of all
new designs are computed.
Dedicated to the memory of the late professor Stefan Dodunekov
on the occasion of his 70th anniversary.
We classify up to multiplier equivalence maximal (v, 3, 1) optical
orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1)
OOCs with v ≤ 99.
There is a one-to-one correspondence between maximal (v, 3, 1) OOCs,
maximal cyclic binary constant weight codes of weight 3 and minimum dis
tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary
cyclically permutable constant...
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