On entropy-like functionals and codes for metrized probability spaces II

Miroslav Katětov

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On entropy-like functionals and codes for metrized probability spaces. I.

Miroslav Katětov (1990)

Commentationes Mathematicae Universitatis Carolinae

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A representation theorem for perfect partitions of $Z^{2}$ -actions with finite entropy

B. Kamiński (1988)

Colloquium Mathematicae

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Exploring invariant linear codes through generators and centralizers

Partha Pratim Dey (2005)

Archivum Mathematicum

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We investigate a $H$ -invariant linear code $C$ over the finite field $F_{p}$ where $H$ is a group of linear transformations. We show that if $H$ is a noncyclic abelian group and $(| H |, p) = 1$ , then the code $C$ is the sum of the centralizer codes $C_{c} (h)$ where $h$ is a nonidentity element of $H$ . Moreover if $A$ is subgroup of $H$ such that $A ≅ Z_{q} \times Z_{q}$ , $q \neq p$ , then dim $C$ is known when the dimension of $C_{c} (K)$ is known for each subgroup $K \neq 1$ of $A$ . In the last few sections we restrict our scope of investigation to a special class of invariant codes,...

On the differential and residual entropy

Miroslav Katětov (1988)

Commentationes Mathematicae Universitatis Carolinae

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Operator entropy inequalities

M. S. Moslehian, F. Mirzapour, A. Morassaei (2013)

Colloquium Mathematicae

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We investigate a notion of relative operator entropy, which develops the theory started by J. I. Fujii and E. Kamei [Math. Japonica 34 (1989), 341-348]. For two finite sequences A = (A₁,...,Aₙ) and B = (B₁,...,Bₙ) of positive operators acting on a Hilbert space, a real number q and an operator monotone function f we extend the concept of entropy by setting $S_{q}^{f} (A | B) : = \sum_{j = 1}^{n} A_{j}^{1 / 2} {(A_{j}^{- 1 / 2} B_{j} A_{j}^{- 1 / 2})}^{q} f (A_{j}^{- 1 / 2} B_{j} A_{j}^{- 1 / 2}) A_{j}^{1 / 2}$ , and then give upper and lower bounds for $S_{q}^{f} (A | B)$ as an extension of an inequality due to T. Furuta [Linear Algebra Appl. 381 (2004),...

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