We investigate the finitary functions from a finite field \(\mathbb {F}_q\) to the finite field \(\mathbb {F}_p\), where p and q are powers of different primes. An \((\mathbb {F}_p,\mathbb {F}_q)\)-linearly closed clonoid is a subset of these functions which is closed under composition from the right and from the left with linear mappings. We give a characterization of these subsets of functions through the invariant subspaces of the vector space \(\mathbb {F}_p^{\mathbb {F}_q\backslash \{0\}}\) with respect to a certain linear transformation with minimal polynomial \(x^{q-1} - 1\). Furthermore we prove that each of these subsets of functions is generated by one unary function.

我们研究了从有限域\（\ mathbb {F} _q \）到有限域\（\ mathbb {F} _p \）的最终函数，其中p和q是不同素数的幂。一个\（（\ mathbb {F} _p，\ mathbb {F} _q）\） -linearly封闭clonoid是这些功能，其根据组合物从右侧和从左侧与线性映射关闭的子集。我们通过向量空间\（\ mathbb {F} _p ^ {\ mathbb {F} _q \反斜杠\ {0 \}} \}的不变子空间相对于某些线性变换来表征这些函数子集具有最小多项式\（x ^ {q-1}-1 \）。此外，我们证明了这些功能子集的每一个都是由一个一元函数生成的。