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Improved lower bounds on the rigidity of Hadamard matrices. (English. Russian original) Zbl 0917.15013
Math. Notes 63, No. 4, 471-475 (1998); translation from Mat. Zametki 63, No. 4, 535-540 (1998).
It is proved that for any \(n\times n\) generalized Hadamard matrix \(H\) and any \(r\leq n/2\) the inequality \(R_H^c(r)\geq \Omega(n^2/r)\) holds. Moreover, if \(\theta\) is an additional parameter satisfying \(\theta\geq n/r\), then \(R_H^c(r,\theta)\geq \Omega(n^3/r\theta^2)\). Here, \(R_H^c(r)\) and \(R_H^c(r,\theta)\) are the rigidity functions of \(H\) while \(\Omega(g)=f\) in \(f(x)\geq cg(x)\) with some positive constant \(c\) for all \(x\) from the domain of the functions \(f\) and \(g\).

MSC:
15A42 Inequalities involving eigenvalues and eigenvectors
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