Recently, linear codes constructed from defining sets have been investigatedextensively and they have many applications. In this paper, for an odd prime$p$, we propose a class of $p$-ary linear codes by choosing a proper definingset. Their weight enumerators and complete weight enumerators are presentedexplicitly. The results show that they are linear codes with three weights andsuitable for the constructions of authentication codes and secret sharingschemes.
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机译：近来，对由定义集构成的线性代码进行了广泛的研究，它们具有许多应用。在本文中，对于奇数质数$ p $，我们通过选择适当的定义集来提出一类$ p $ -ary线性代码。明确列出了它们的重量枚举器和完整的重量枚举器。结果表明，它们是具有三个权重的线性代码，适用于认证代码和秘密共享方案的构造。
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