39,397 research outputs found
On the Optimality of the Golden Code
In this note, we prove the optimality
of the Golden Code inside the class of cyclic algebras
based codes. In doing so, we get better insight on
these algebraic codes, not only in dimension 2, but
more generally for higher dimension, and summarizing
the different approaches tried so far to optimize
them, we derive design strategies that we believe are
the key to either show the optimality of existing codes
or give a way to improve them
Information geometric complexity of a trivariate Gaussian statistical model
We evaluate the information geometric complexity of entropic motion on
low-dimensional Gaussian statistical manifolds in order to quantify how
difficult is making macroscopic predictions about a systems in the presence of
limited information. Specifically, we observe that the complexity of such
entropic inferences not only depends on the amount of available pieces of
information but also on the manner in which such pieces are correlated.
Finally, we uncover that for certain correlational structures, the
impossibility of reaching the most favorable configuration from an entropic
inference viewpoint, seems to lead to an information geometric analog of the
well-known frustration effect that occurs in statistical physics.Comment: 16 pages, 1 figur
From the function-sheaf dictionary to quasicharacters of -adic tori
We consider the rigid monoidal category of character sheaves on a smooth
commutative group scheme over a finite field and expand the scope of
the function-sheaf dictionary from connected commutative algebraic groups to
this setting. We find the group of isomorphism classes of character sheaves on
and show that it is an extension of the group of characters of by a
cohomology group determined by the component group scheme of . We also
classify all morphisms in the category character sheaves on . As an
application, we study character sheaves on Greenberg transforms of locally
finite type N\'eron models of algebraic tori over local fields. This provides a
geometrization of quasicharacters of -adic tori.Comment: Added examples and incorporated referee's suggestions. To be
published in Journal of the Institute of Mathematics of Jussie
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