We study a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type whose simple current modules are graded by ${\mathbb{Z}}_{2k}$. Based on those simple current modules, a vertex operator algebra associated with a ${\mathbb{Z}}_{2k}$-code is constructed. The classification of irreducible modules for such a vertex operator algebra is established. Furthermore, all the irreducible modules are realized in a module for a certain lattice vertex operator algebra.

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${\mathbb{ž}}_{2ķ}$代码顶点算子代数

我们研究一种简单，自我对立，理性且 $C_2$CFT型的-有限顶点算子代数，其简单电流模块由 ${\mathbb{ž}}_{2ķ}$。基于这些简单的当前模块，顶点运算符代数与${\mathbb{ž}}_{2ķ}$-code被构建。建立了此类顶点算子代数的不可约模块的分类。此外，所有不可约模块都在某个晶格顶点算子代数的模块中实现。