A set $X\subseteq {\mathrm{\Sigma }}^{++}$ of rectangular pictures over an alphabet Σ is a two-dimensional code if any picture over Σ is tilable in at most one way with pictures in X. Finite strong prefix codes were introduced as a family of decidable two-dimensional codes. We consider infinite strong prefix codes and give a characterization for the maximal ones based on the iterated extensions. Moreover, we study some properties related to the measure of these codes of pictures and prove some connections with the codes of strings.

中文翻译：

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无限二维强前缀码的表征和度量

一套 $X\subseteq {\mathrm{\Sigma }}^{++}$如果∑上的任何图片最多可以用X的方式平铺，则字母表∑上的矩形图片的二维码是二维代码。有限强前缀码作为一组可确定的二维码被引入。我们考虑无限强前缀码，并基于迭代扩展给出最大前缀码的表征。此外，我们研究了与图片的这些代码的度量有关的一些属性，并证明了与字符串的代码之间的某些联系。