We obtain an explicit criterion for p-ary functions to produce association schemes in terms of their Walsh spectrum. Employing this characterization, we explicitly find a correlation between p-ary bent functions and association schemes; to be more exact, we prove that a p-ary bent function induces a p-class association scheme if and only if the function is weakly regular. As applications of our main criterion, we construct many infinite families of few-class association schemes arising from p-ary functions. Furthermore, we present four classes of p-ary two-weight linear codes, which are constructed from the association schemes produced in this paper.

中文翻译：

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用关联方案表征 p 元函数及其应用

我们获得了 p-ary 函数的明确标准，以根据其 Walsh 谱生成关联方案。利用这种特征，我们明确地发现了 p-ary 弯曲函数和关联方案之间的相关性；更准确地说，我们证明了当且仅当函数是弱正则时，p-arybent 函数会引发 p-类关联方案。作为我们主要标准的应用，我们构造了许多由 p-ary 函数产生的少数类关联方案的无限族。此外，我们提出了四类 p 元二权线性码，它们是根据本文产生的关联方案构造的。