In this paper, for an odd prime p, by extending Li et al.'s construction [17], several classes of two-weight and three-weight linear codes over the finite field ${\mathbb{F}}_p$ are constructed from a defining set, and then their complete weight enumerators are determined by using Weil sums. Furthermore, we show that some examples of these codes are optimal or almost optimal with respect to the Griesmer bound. Our results generalize the corresponding results in [15], [17].

中文翻译：

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几类二权重和三权重线性代码的完整权重枚举器

在本文中，对于奇素数p，通过扩展 Li 等人的构造 [17]，有限域上的几类二权重和三权重线性代码${\mathbb{F}}_{磷}$由定义集构造，然后使用 Weil 和确定它们的完整权重枚举数。此外，我们表明这些代码的一些示例对于 Griesmer 边界是最佳的或几乎是最佳的。我们的结果概括了 [15]、[17] 中的相应结果。