We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if their feedback polynomials are relatively prime. Then, we characterize the appropriate parameters for a family of pairwise coprime polynomials to generate a partial spread required for the support of a bent function, showing that such families exist if and only if the degrees of the underlying polynomials are either 1 or 2. We then count the resulting sets of polynomials and prove that, for degree 1, our LRS construction coincides with the Desarguesian partial spread. Finally, we perform a computer search of all \(\mathcal{PS}\mathcal{}^-\) and \(\mathcal{PS}\mathcal{}^+\) bent functions of \(n=8\) variables generated by our construction and compute their 2-ranks. The results show that many of these functions defined by polynomials of degree \(d=2\) are not EA-equivalent to any Maiorana–McFarland or Desarguesian partial spread function.

我们使用由线性循环序列 (LRS) 生成的子空间来构建部分扩展弯曲函数。我们首先表明，当且仅当它们的反馈多项式互质时，由两个 LRS 定义的线性映射的核具有平凡的交集。然后，我们描述了成对互质多项式族的适当参数，以生成支持弯曲函数所需的部分扩展，表明当且仅当基础多项式的度数为 1 或 2 时，此类族才存在。我们然后计算得到的多项式集并证明，对于 1 次，我们的 LRS 构造与 Desarguesian 部分扩展一致。最后，我们对所有\(\mathcal{PS}\mathcal{}^-\)和\(\mathcal{PS}\mathcal{}^+\)我们的构造生成的\(n=8\)变量的弯曲函数并计算它们的 2 秩。结果表明，由\(d=2\)次多项式定义的这些函数中的许多都不是 EA 等价于任何 Maiorana-McFarland 或 Desarguesian 部分扩展函数。