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Suzuki-invariant codes from the Suzuki curve
In this paper we consider the Suzuki curve over
the field with elements. The automorphism group of this curve is
known to be the Suzuki group with elements. We
construct AG codes over from a -invariant divisor
, giving an explicit basis for the Riemann-Roch space for . These codes then have the full Suzuki group as their
automorphism group. These families of codes have very good parameters and are
explicitly constructed with information rate close to one. The dual codes of
these families are of the same kind if
The de Rham cohomology of the Suzuki curves
For a natural number , let be the th
Suzuki curve. We study the mod Dieudonn\'{e} module of ,
which gives the equivalent information as the Ekedahl-Oort type or the
structure of the -torsion group scheme of its Jacobian. We accomplish this
by studying the de Rham cohomology of . For all , we
determine the structure of the de Rham cohomology as a -modular
representation of the th Suzuki group and the structure of a submodule of
the mod Dieudonn\'{e} module. For and , we determine the complete
structure of the mod Dieudonn\'{e} module
Evolving Nuclear Many-Body Forces with the Similarity Renormalization Group
In recent years, the Similarity Renormalization Group has provided a powerful
and versatile means to soften interactions for ab initio nuclear calculations.
The substantial contribution of both induced and initial three-body forces to
the nuclear interaction has required the consistent evolution of free-space
Hamiltonians in the three-particle space. We present the most recent progress
on this work, extending the calculational capability to the p-shell nuclei and
showing that the hierarchy of induced many-body forces is consistent with
previous estimates. Calculations over a range of the flow parameter for 6Li,
including fully evolved NN+3N interactions, show moderate contributions due to
induced four-body forces and display the same improved convergence properties
as in lighter nuclei. A systematic analysis provides further evidence that the
hierarchy of many-body forces is preserved.Comment: 26 pages, 15 figures, and 5 table
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