论文标题
Zeta功能张量代码
Zeta Functions for Tensor Codes
论文作者
论文摘要
在这项工作中，我们介绍了与Ravagnani-type dopodes相关的新一类最佳张量代码，即$ j $ -tensor的最大等级距离代码。我们表明，它扩展了$ j $ - 最大排名距离代码，并包含$ j $ - tensor二项制矩确定的代码（相对于Ravagnani-type type dopodes）作为适当的子类。我们定义和研究张量代码的广义Zeta函数。我们建立了该对象与ravagnani-type激体代码的重量枚举者之间的联系。我们介绍了张量代码不变的新细化，以利用某些类别的一类动物的产品晶格结构，并得出相应的Macwilliams身份。在此框架中，我们还定义了张量枚举器的多元版本，并与相应的Zeta函数建立了关系。作为应用，我们得出了与Delsarte和Ravagnani-Type反码相关的广义张量重量的连接。
In this work we introduce a new class of optimal tensor codes related to the Ravagnani-type anticodes, namely the $j$-tensor maximum rank distance codes. We show that it extends the family of $j$-maximum rank distance codes and contains the $j$-tensor binomial moment determined codes (with respect to the Ravagnani-type anticodes) as a proper subclass. We define and study the generalized zeta function for tensor codes. We establish connections between this object and the weight enumerator of a code with respect to the Ravagnani-type anticodes. We introduce a new refinement of the invariants of tensor codes exploiting the structure of product lattices of some classes of anticodes and we derive the corresponding MacWilliams identities. In this framework, we also define a multivariate version of the tensor weight enumerator and we establish relations with the corresponding zeta function. As an application we derive connections on the generalized tensor weights related to the Delsarte and Ravagnani-type anticodes.
