In this paper, we give a representation of the average of complete joint weight enumerators of two linear codes of length n over \(\mathbb {F}_q\) and \(\mathbb {Z}_k\) in terms of the compositions of n and their distributions in the codes. We also obtain a generalization of the representation for the average of g-fold complete joint weight enumerators of codes over \(\mathbb {F}_q\) and \(\mathbb {Z}_{k}\). Finally, the average of intersection numbers of a pair of Type \(\mathrm{{III}}\) (resp. Type \(\mathrm{{IV}}\)) codes, and its second moment are found.

中文翻译：

---

完整联合体重调查员和自我对偶代码的平均值

在本文中，我们给出了平均的长度的两个线性码完整关节重量枚举的表示 Ñ超过\（\ mathbb {F} _q \）和\（\ mathbb {Z} _K \）在组合物中的术语的ñ和它们在代码分布。我们还获得了\（\ mathbb {F} _q \）和\（\ mathbb {Z} _ {k} \）上g倍完整联合权重枚举数的平均值的表示形式的概括。最后，找到一对类型\（\ mathrm {{III}} \）（分别为 \（\ mathrm {{IV}} \））代码的相交数的平均值 及其第二矩。