13,273 research outputs found
Framed vertex operator algebras, codes and the moonshine module
For a simple vertex operator algebra whose Virasoro element is a sum of
commutative Virasoro elements of central charge 1/2, two codes are introduced
and studied. It is proved that such vertex operator algebras are rational. For
lattice vertex operator algebras and related ones, decompositions into direct
sums of irreducible modules for the product of the Virasoro algebras of central
charge 1/2 are explicitly described. As an application, the decomposition of
the moonshine vertex operator algebra is obtained for a distinguished system of
48 Virasoro algebras.Comment: Latex, 54 page
Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids
To each linear code over a finite field we associate the matroid of its
parity check matrix. We show to what extent one can determine the generalized
Hamming weights of the code (or defined for a matroid in general) from various
sets of Betti numbers of Stanley-Reisner rings of simplicial complexes
associated to the matroid
- …