130 research outputs found
Orthogonal Macroelement Scaling Vectors and Wavelets in 1-D
We develop a {\em macroelement} based technique for constructing orthogonal univariate multiwavelets. We illustrate the technique with two examples. In the first example we provide a new construction of the symmetric, orthogonal, continuous scaling vector given in \cite{GHM}. In the second example, we construct a continuous orthogonal scaling vector with three components. The components of this scaling vector are symmetric or antisymmetric and provide approximation order 3, (equivalently, the components of are orthogonal to polynomials of degree 2 or less.) We believe this second example to be new
Energy bounds for codes and designs in Hamming spaces
We obtain universal bounds on the energy of codes and for designs in Hamming
spaces. Our bounds hold for a large class of potential functions, allow unified
treatment, and can be viewed as a generalization of the Levenshtein bounds for
maximal codes.Comment: 25 page
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