Let $S$ be a set of arbitrary objects, and let $S^d=\{v_1...v_d:v_i\in S\}$. A polybox code is a set $V\subset S^d$ with the property that for every two words $v,w\in V$ there is $i\in \left[d\right]$ with $v_i^{\prime }=w_i$, where a permutation $s\mapsto s^{\prime }$ of $S$ is such that $s^{\prime \prime }={\left(s^{\prime }\right)}^{\prime }=s$ and $s^{\prime }\ne s$. If $\left|V\right|=2^d$, then $V$ is called a cube tiling code. Cube tiling codes determine 2-periodic cube tilings of ${\mathbb{R}}^d$ or, equivalently, tilings of the flat torus ${\mathbb{T}}^d=\{(x_1,\dots ,x_d)\left(\mathrm{mod}2\right):(x_1,\dots ,x_d)\in {\mathbb{R}}^d\}$ by translates of the unit cube as well as $r$-perfect codes in ${\mathbb{Z}}_{4r+2}^d$ in the maximum metric. By a structural result, cube tiling codes for $d=4$ are enumerated. It is computed that there are 27,385 non-isomorphic cube tiling codes in dimension four, and the total number of such codes is equal to $17,794,836,080,455,680$. Moreover, some procedure of passing from a cube tiling code to a cube tiling code in dimensions $d\le 5$ is given.

让 $\mathrm{小号}$ 是一组任意对象，然后让 ${\mathrm{小号}}^d=\{v_{\mathrm{1个}}。。。v_d：v_{\mathrm{一世}}\in \mathrm{小号}\}$。多重框代码​​是一组$V\subset {\mathrm{小号}}^d$ 具有每两个字的属性 $v，w\in V$ 有 $\mathrm{一世}\in \left[d\right]$ 与 $v_{\mathrm{一世}}^{\prime }=w_{\mathrm{一世}}$，其中排列 $s\mapsto s^{\prime }$ 的 $\mathrm{小号}$ 就是这样 $s^{\prime \prime }={（s^{\prime }）}^{\prime }=s$ 和 $s^{\prime }\ne s$。如果$\left|V\right|=2^d$， 然后 $V$被称为多维数据集切片代码。多维数据集切片代码确定${\mathbb{[R}}^d$ 或等效地，扁平圆环的平铺 ${\mathbb{Ť}}^d=\{（X_{\mathrm{1个}}，\dots ，X_d）（\mathrm{模}2）：（X_{\mathrm{1个}}，\dots ，X_d）\in {\mathbb{[R}}^d\}$ 通过单位立方的转换以及 $\mathrm{[R}$完美的代码 ${\mathbb{ž}}_{4\mathrm{[R}+2}^d$在最大指标中。根据结构结果，多维数据集切片代码$d=4$被枚举。计算出在第4维上有27385个非同构立方体平铺代码，这些代码的总数等于$17，794，836，080，455，680$。此外，从多维数据集切片代码传递到多维数据集切片代码的一些过程$d\le 5$ 给出。