有限字母表上的 Diletter 循环码。
Diletter circular codes over finite alphabets.
机构信息
Institute of Mathematical Biology, Faculty for Computer Sciences, University of Applied Sciences 68163 Mannheim, Germany.
Theoretical Bioinformatics, ICube, University of Strasbourg, CNRS, 300 Boulevard Sébastien Brant 67400 Illkirch, France.
出版信息
Math Biosci. 2017 Dec;294:120-129. doi: 10.1016/j.mbs.2017.10.001. Epub 2017 Oct 10.
The graph approach of circular codes recently developed (Fimmel et al., 2016) allows here a detailed study of diletter circular codes over finite alphabets. A new class of circular codes is identified, strong comma-free codes. New theorems are proved with the diletter circular codes of maximal length in relation to (i) a characterisation of their graphs as acyclic tournaments; (ii) their explicit description; and (iii) the non-existence of other maximal diletter circular codes. The maximal lengths of paths in the graphs of the comma-free and strong comma-free codes are determined. Furthermore, for the first time, diletter circular codes are enumerated over finite alphabets. Biological consequences of dinucleotide circular codes are analysed with respect to their embedding in the trinucleotide circular code X identified in genes and to the periodicity modulo 2 observed in introns. An evolutionary hypothesis of circular codes is also proposed according to their combinatorial properties.
最近开发的循环码的图方法（Fimmel 等人，2016）允许在这里详细研究有限字母表上的双字母循环码。确定了一类新的循环码，即强无逗号码。用最长的双字母循环码证明了新的定理，这些定理与（i）它们的图作为非循环竞赛图的特征化；（ii）它们的显式描述；以及（iii）不存在其他最大的双字母循环码有关。确定了无逗号和强无逗号码的图中路径的最大长度。此外，这是第一次对有限字母表上的双字母循环码进行枚举。还根据双字母循环码在基因中确定的三字母循环码 X 中的嵌入以及在内含子中观察到的 2 模周期，分析了双核苷酸循环码的生物学后果。还根据它们的组合性质提出了循环码的进化假设。
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