12,167 research outputs found
Design Lines
The two basic equations satisfied by the parameters of a block design define
a three-dimensional affine variety in . A point
of that is not in some sense trivial lies on four lines lying in
. These lines provide a degree of organization for certain general
classes of designs, and the paper is devoted to exploring properties of the
lines. Several examples of families of designs that seem naturally to follow
the lines are presented.Comment: 16 page
Classification of generalized Hadamard matrices H(6,3) and quaternary Hermitian self-dual codes of length 18
All generalized Hadamard matrices of order 18 over a group of order 3,
H(6,3), are enumerated in two different ways: once, as class regular symmetric
(6,3)-nets, or symmetric transversal designs on 54 points and 54 blocks with a
group of order 3 acting semi-regularly on points and blocks, and secondly, as
collections of full weight vectors in quaternary Hermitian self-dual codes of
length 18. The second enumeration is based on the classification of Hermitian
self-dual [18,9] codes over GF(4), completed in this paper. It is shown that up
to monomial equivalence, there are 85 generalized Hadamard matrices H(6,3), and
245 inequivalent Hermitian self-dual codes of length 18 over GF(4).Comment: 17 pages. Minor revisio
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