
On some automorphisms of rational functions and their applications in rank metric codes
Recently, there is a growing interest in the study of rank metric codes....
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New Constructions of Subspace Codes Using Subsets of MRD codes in Several Blocks
A basic problem for the constant dimension subspace coding is to determi...
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Fundamental Properties of SumRank Metric Codes
This paper investigates the theory of sumrank metric codes for which th...
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Lifted codes and the multilevel construction for constant dimension codes
Constant dimension codes are e.g. used for error correction and detectio...
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On symmetric and Hermitian rank distance codes
Let M denote the set S_n, q of n × n symmetric matrices with entries in ...
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Tensor Representation of RankMetric Codes
We present the theory of rankmetric codes with respect to the 3tensors...
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Constructing Object Groups Corresponding to Concepts for Recovery of a Summarized Sequence Diagram
Comprehending the behavior of an objectoriented system solely from its ...
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Maximal Ferrers Diagram Codes: Constructions and Genericity Considerations
This paper investigates the construction of rankmetric codes with specified Ferrers diagram shapes. These codes play a role in the multilevel construction for subspace codes. A conjecture from 2009 provides an upper bound for the dimension of a rankmetric code with given specified Ferrers diagram shape and rank distance. While the conjecture in its generality is wide open, several cases have been established in the literature. This paper contributes further cases of Ferrers diagrams and ranks for which the conjecture holds true. In addition, probabilities for maximal Ferrers diagram codes and MRD codes are investigated. It is shown that for growing field size the limiting probability for the event that randomly chosen matrices with given shape generate a maximal Ferrers diagram code, depends highly on the Ferrers diagram. For instance, for [m x 2]MRD codes with rank 2 this limiting probability is close to 1/e.
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