Generalized $p$-ary $\text{cPS}$ Bent Functions

We use $m$-dimensional partial spreads of ${\text{fp}}^{2n}$, where $p$ is an odd prime, $n$ is a positive integer and $m$ divides $n$, to construct two classes of bent functions from ${\text{fp}}^{2n}$ to $\text{fp}$. Our construction generalizes the classes of $p$-ary ${\text{cPS}}^{-}$ and ${\text{cPS}}^{+}$ bent functions proposed by P. Lison\v ek and H. Y. Lu (Des. Codes Cryptogr. 73 (2014), 209–216).