939 research outputs found
MRD codes with maximum idealizers
Left and right idealizers are important invariants of linear rank-distance
codes. In the case of maximum rank-distance (MRD for short) codes in
the idealizers have been proved to be isomorphic to
finite fields of size at most . Up to now, the only known MRD codes with
maximum left and right idealizers are generalized Gabidulin codes, which were
first constructed in 1978 by Delsarte and later generalized by Kshevetskiy and
Gabidulin in 2005. In this paper we classify MRD codes in
for with maximum left and right idealizers
and connect them to Moore-type matrices. Apart from generalized Gabidulin
codes, it turns out that there is a further family of rank-distance codes
providing MRD ones with maximum idealizers for , odd and for ,
. These codes are not equivalent to any previously known MRD
code. Moreover, we show that this family of rank-distance codes does not
provide any further examples for .Comment: Reviewers' comments implemented, we changed the titl
A Transferable Machine-Learning Model of the Electron Density
The electronic charge density plays a central role in determining the
behavior of matter at the atomic scale, but its computational evaluation
requires demanding electronic-structure calculations. We introduce an
atom-centered, symmetry-adapted framework to machine-learn the valence charge
density based on a small number of reference calculations. The model is highly
transferable, meaning it can be trained on electronic-structure data of small
molecules and used to predict the charge density of larger compounds with low,
linear-scaling cost. Applications are shown for various hydrocarbon molecules
of increasing complexity and flexibility, and demonstrate the accuracy of the
model when predicting the density on octane and octatetraene after training
exclusively on butane and butadiene. This transferable, data-driven model can
be used to interpret experiments, initialize electronic structure calculations,
and compute electrostatic interactions in molecules and condensed-phase
systems
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