229 research outputs found
Supplementary difference sets with symmetry for Hadamard matrices
First we give an overview of the known supplementary difference sets (SDS)
(A_i), i=1..4, with parameters (n;k_i;d), where k_i=|A_i| and each A_i is
either symmetric or skew and k_1 + ... + k_4 = n + d. Five new Williamson
matrices over the elementary abelian groups of order 25, 27 and 49 are
constructed. New examples of skew Hadamard matrices of order 4n for n=47,61,127
are presented. The last of these is obtained from a (127,57,76)-difference
family that we have constructed. An old non-published example of G-matrices of
order 37 is also included.Comment: 16 pages, 2 tables. A few minor changes are made. The paper will
appear in Operators and Matrice
Self-Dual codes from -matrices of skew symmetric type
Previously, self-dual codes have been constructed from weighing matrices, and
in particular from conference matrices (skew and symmetric). In this paper,
codes constructed from matrices of skew symmetric type whose determinants reach
the Ehlich-Wojtas' bound are presented. A necessary and sufficient condition
for these codes to be self-dual is given, and examples are provided for lengths
up to 52
Implementing Brouwer's database of strongly regular graphs
Andries Brouwer maintains a public database of existence results for strongly
regular graphs on vertices. We implemented most of the infinite
families of graphs listed there in the open-source software Sagemath, as well
as provided constructions of the "sporadic" cases, to obtain a graph for each
set of parameters with known examples. Besides providing a convenient way to
verify these existence results from the actual graphs, it also extends the
database to higher values of .Comment: 18 pages, LaTe
Grassmannian Frames with Applications to Coding and Communication
For a given class of uniform frames of fixed redundancy we define
a Grassmannian frame as one that minimizes the maximal correlation among all frames . We first analyze
finite-dimensional Grassmannian frames. Using links to packings in Grassmannian
spaces and antipodal spherical codes we derive bounds on the minimal achievable
correlation for Grassmannian frames. These bounds yield a simple condition
under which Grassmannian frames coincide with uniform tight frames. We exploit
connections to graph theory, equiangular line sets, and coding theory in order
to derive explicit constructions of Grassmannian frames. Our findings extend
recent results on uniform tight frames. We then introduce infinite-dimensional
Grassmannian frames and analyze their connection to uniform tight frames for
frames which are generated by group-like unitary systems. We derive an example
of a Grassmannian Gabor frame by using connections to sphere packing theory.
Finally we discuss the application of Grassmannian frames to wireless
communication and to multiple description coding.Comment: Submitted in June 2002 to Appl. Comp. Harm. Ana
Finding D-optimal designs by randomised decomposition and switching
A square {+1,-1}-matrix of order n with maximal determinant is called a saturated D-optimal design. We consider some cases of saturated Doptimal designs where n > 2, n ≢ 0 mod 4, so the Hadamard bound is not attainable, but bounds due to Barba or Ehlic
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