论文标题
Matroids II的谐波tutte多项式
Harmonic Tutte polynomials of matroids II
论文作者
论文摘要
在这项工作中，我们介绍了有限的Frobenius戒指的代码枚举$ M $ tuple列出的谐音概括。还给出了有限的Frobenius戒指代码的MacWilliams-type身份的谐音版本。此外，我们定义了来自Matroid理论的众所周知多项式的甲状腺类似物，即Tutte多项式和串联多项式，并将它们与谐波功能相关联。我们还证明了将这些多项式与有限的Frobenius戒指相比，代码枚举的谐波$ M $ M $ M-Tuple枚举者有关的Greene型身份。作为这种绿色型身份的应用，我们为谐波$ m $ m $ tuple的重量枚举者提供了一个简单的组合证明，比有限的frobenius戒指。最后，我们提供了相对不变的空间的结构，其中包含有限字段上自动划分代码的谐波$ m $ tuple重量枚举者。
In this work, we introduce the harmonic generalization of the $m$-tuple weight enumerators of codes over finite Frobenius rings. A harmonic version of the MacWilliams-type identity for $m$-tuple weight enumerators of codes over finite Frobenius ring is also given. Moreover, we define the demi-matroid analogue of well-known polynomials from matroid theory, namely Tutte polynomials and coboundary polynomials, and associate them with a harmonic function. We also prove the Greene-type identity relating these polynomials to the harmonic $m$-tuple weight enumerators of codes over finite Frobenius rings. As an application of this Greene-type identity, we provide a simple combinatorial proof of the MacWilliams-type identity for harmonic $m$-tuple weight enumerators over finite Frobenius rings. Finally, we provide the structure of the relative invariant spaces containing the harmonic $m$-tuple weight enumerators of self-dual codes over finite fields.
