The dual of the Kasami code of length $q^{2}-1$ , with $q$ a power of 2, is constructed by concatenating a cyclic MDS code of length $q+1$ over $F_{q}$ with a Simplex code of length $q-1$ . This yields a new derivation of the weight distribution of the Kasami code, a new description of its coset graph, and a new proof that the Kasami code is completely regular. The automorphism groups of the Kasami code and the related $q$ -ary MDS code are determined. New cyclic completely regular codes over finite fields a power of 2, generalized Kasami codes, are constructed; they have coset graphs isomorphic to that of the Kasami codes. Another wide class of completely regular codes, including additive codes, as well as unrestricted codes, is obtained by combining cosets of the Kasami or generalized Kasami code.

中文翻译：

---

类型 2 的 Kasami 代码的一种新方法

Kasami 长度码的对偶 $q^{2}-1$ ， 和 $q$ 一个 2 的幂，是通过连接一个长度为 1 的循环 MDS 码来构造的 $q+1$ 超过 $F_{q}$ 带有长度的单工代码 $q-1$ . 这产生了 Kasami 代码权重分布的新推导、其陪集图的新描述以及 Kasami 代码完全正则的新证明。Kasami 码的自同构群及其相关 $q$ -ary MDS 代码被确定。构造了有限域上的新循环完全正则码 2 的幂，广义 Kasami 码；它们具有与 Kasami 码同构的陪集图。通过组合 Kasami 或广义 Kasami 代码的陪集获得另一类完全规则的代码，包括加性代码以及非限制性代码。