Frames, graphs and erasures

• Published in: Linear algebra and its applications Vol. 404; pp. 118 - 146
• Main Authors: Bodmann, Bernhard G., Paulsen, Vern I.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.07.2005; Elsevier Science
• Subjects: Algebra; Codes; Conference matrix; Erasures; Error bounds; Exact sciences and technology; Frames; Graphs; Hadamard matrix; Linear and multilinear algebra, matrix theory; Mathematics; Sciences and techniques of general use; Two-graphs; Frames; Codes; Erasures; Primary 46L05; 47A20; Hadamard matrix; Secondary 46A22; Conference matrix; Error bounds; Graphs; 46M10; Two-graphs; 46H25; Error estimation; 47A20 Frames; Error bound; Erasure; Graph theory; Code; Equivalence classes; Coding; Primary; Hadamard transformation

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...