Association schemes play an important role in algebraic combinatorics and have important applications in coding theory, graph theory and design theory. The methods to construct association schemes by using bent functions have been extensively studied. Recently, in Özbudak and Pelen (J Algebr Comb 56:635–658, 2022), Özbudak and Pelen constructed infinite families of symmetric association schemes of classes 5 and 6 by using ternary non-weakly regular bent functions. They also stated that “constructing 2p-class association schemes from p-ary non-weakly regular bent functions is an interesting problem", where \(p>3\) is an odd prime. In this paper, using non-weakly regular bent functions, we construct infinite families of symmetric association schemes of classes 2p, \((2p+1)\) and \(\frac{3p+1}{2}\) for any odd prime p. Fusing those association schemes, we obtain t-class symmetric association schemes, where \(t=4,5,6,7\). In addition, we give the sufficient and necessary conditions for the partitions P, D, T, U and V (defined in this paper) to induce symmetric association schemes.

关联方案在代数组合学中起着重要作用，在编码理论、图论和设计理论中也有重要的应用。使用 bent 函数构造关联方案的方法已经被广泛研究。最近，在 Özbudak 和 Pelen （J Algebr Comb 56：635–658， 2022） 中，Özbudak 和 Pelen 通过使用三元非弱正则弯曲函数构建了第 5 类和第 6 类对称关联方案的无限族。他们还指出，“从 p-ary 非弱正则弯曲函数构造 2 个p 类关联方案是一个有趣的问题”，其中 \（p>3\） 是一个奇数素数。在本文中，使用非弱正则弯曲函数，我们为任何奇数素数 p 构建了类 2p、\（（2p+1）\） 和 \（\frac{3p+1}{2}\） 的无限对称关联方案族。融合这些关联方案，我们得到了 t 类对称关联方案，其中 \（t=4,5,6,7\）。此外，我们为分区 P、D、T、U 和 V（在本文中定义）提供了充分和必要的条件，以诱导对称关联方案。