In a previous paper (see [3]) we determined the values of the next-to-minimal Hamming weights of affine cartesian codes of order d, for almost all values of d. In the present paper we determine the next-to-minimal weights for the missing values of d, assuming that the sets in the cartesian product which appears in the definition of the code are subfields of ${\mathbb{F}}_q$.

中文翻译：

---

完成仿射笛卡尔代码的次最小权重的确定

在以前的文件（见[3]），我们确定的顺序的仿射笛卡尔码的下一个到最小汉明权重的值d，对于几乎所有的值d。在本文中，假设代码定义中出现的笛卡尔积中的集合是的子字段，我们确定d的缺失值的次最小权重。${\mathbb{F}}_q$。