113 research outputs found
The Gewirtz graph: An exercise in the theory of graph spectra
Graphs;mathematics
Frames, Graphs and Erasures
Two-uniform frames and their use for the coding of vectors are the main
subject of this paper. These frames are known to be optimal for handling up to
two erasures, in the sense that they minimize the largest possible error when
up to two frame coefficients are set to zero. Here, we consider various
numerical measures for the reconstruction error associated with a frame when an
arbitrary number of the frame coefficients of a vector are lost. We derive
general error bounds for two-uniform frames when more than two erasures occur
and apply these to concrete examples. We show that among the 227 known
equivalence classes of two-uniform (36,15)-frames arising from Hadamard
matrices, there are 5 that give smallest error bounds for up to 8 erasures.Comment: 28 pages LaTeX, with AMS macros; v.3: fixed Thm 3.6, added comment,
Lemma 3.7 and Proposition 3.8, to appear in Lin. Alg. App
A design and a code invariant under the simple group Co3
Mathematics;mathematics
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