摘要翻译：
用矩阵形式表示分子遗传字母表的多级系统，揭示了该系统的代数性质。遗传(4*4)-和(8*8)-矩阵家族显示了遗传系统与Walsh函数和Hadamard矩阵的意外联系，这些联系在抗噪编码、数字通信和数字全息理论中已知。这种遗传矩阵的并矢移位分解导致稀疏矩阵集。这些集合中的每一个都是关于乘法的闭集，并定义了相关的超复数代数。证明了在单位坐标下，遗传Hadamard矩阵与Hamilton四元数及其复化的矩阵表示是相同的。从遗传代数的角度分析了已知方言的遗传密码多样性。给出了遗传特性的Punnett平方的代数类比。我们的结果用于分析遗传现象。在布尔函数系统谱逻辑的基础上，提出了DNA和表观遗传学中基因逻辑代码的存在性。我们的结果显示了发展代数逻辑生物学的有希望的方法，特别是在沃尔什函数上的逻辑全息方面。
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英文标题：
《The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts》
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作者：
Sergey V. Petoukhov
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最新提交年份：
2016
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. Families of genetic (4*4)- and (8*8)-matrices show unexpected connections of the genetic system with Walsh functions and Hadamard matrices, which are known in theory of noise-immunity coding, digital communication and digital holography. Dyadic-shift decompositions of such genetic matrices lead to sets of sparse matrices. Each of these sets is closed in relation to multiplication and defines relevant algebra of hypercomplex numbers. It is shown that genetic Hadamard matrices are identical to matrix representations of Hamilton quaternions and its complexification in the case of unit coordinates. The diversity of known dialects of the genetic code is analyzed from the viewpoint of the genetic algebras. An algebraic analogy with Punnett squares for inherited traits is shown. Our results are used in analyzing genetic phenomena. The statement about existence of the geno-logic code in DNA and epigenetics on the base of the spectral logic of systems of Boolean functions is put forward. Our results show promising ways to develop algebraic-logical biology, in particular, in connection with the logic holography on Walsh functions.
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PDF链接：
https://arxiv.org/pdf/1102.3596