The $X$ motifs, motifs from the circular code $X$, are enriched in the (protein coding) genes of bacteria, archaea, eukaryotes, plasmids and viruses, moreover, in the minimal gene set belonging to the three domains of life, as well as in tRNA and rRNA sequences. They allow to retrieve, maintain and synchronize the reading frame in genes, and contribute to the regulation of gene expression. These results lead here to a theoretical study of genes based on the circular code alphabet. A new occurrence relation of the circular code $X$ under the hypothesis of an equiprobable (balanced) strand pairing is given. Surprisingly, a statistical analysis of a large set of bacterial genes retrieves this relation on the circular code alphabet, but not on the DNA alphabet. Furthermore, the circular code $X$ has the strongest balanced circular code pairing among 216 maximal $C^3$ self-complementary trinucleotide circular codes, a new property of this circular code $X$. As an application of this theory, different tRNAs studied on the circular code alphabet reveal an unexpected stem structure. Thus, the circular code $X$ would have constructed a coding stem in tRNAs as an outline of the future gene structure and the future DNA double helix.

这 $X$ 图案，来自圆形代码的图案 $X$, 富含细菌、古细菌、真核生物、质粒和病毒的（蛋白质编码）基因，此外，还富含属于生命三个领域的最小基因集，以及 tRNA 和 rRNA 序列。它们允许检索、维持和同步基因中的阅读框，并有助于基因表达的调节。这些结果导致了基于循环代码字母表的基因的理论研究。循环码的新出现关系$X$在等概率（平衡）链配对的假设下给出。令人惊讶的是，对大量细菌基因的统计分析在循环代码字母表上检索到了这种关系，但在 DNA 字母表上却没有。此外，循环代码$X$ 在最大的216个中拥有最强的平衡循环码对 $C^3$ 自互补三核苷酸循环代码，该循环代码的新特性 $X$. 作为该理论的应用，在循环代码字母表上研究的不同 tRNA 揭示了意想不到的茎结构。因此，循环代码$X$ 将在 tRNA 中构建一个编码茎，作为未来基因结构和未来 DNA 双螺旋的轮廓。