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The Genetic Code, Hadamard Matrices, Noise Immunity, and Quantum Computers

The Genetic Code, Hadamard Matrices, Noise Immunity, and Quantum Computers

Sergey Petoukhov, Matthew He
Copyright: © 2010 |Pages: 17
ISBN13: 9781605661247|ISBN10: 1605661244|ISBN13 Softcover: 9781616924065|EISBN13: 9781605661254
DOI: 10.4018/978-1-60566-124-7.ch006
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MLA

Sergey Petoukhov and Matthew He. "The Genetic Code, Hadamard Matrices, Noise Immunity, and Quantum Computers." Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics: Advanced Patterns and Applications, IGI Global, 2010, pp.115-131. https://doi.org/10.4018/978-1-60566-124-7.ch006

APA

S. Petoukhov & M. He (2010). The Genetic Code, Hadamard Matrices, Noise Immunity, and Quantum Computers. IGI Global. https://doi.org/10.4018/978-1-60566-124-7.ch006

Chicago

Sergey Petoukhov and Matthew He. "The Genetic Code, Hadamard Matrices, Noise Immunity, and Quantum Computers." In Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics: Advanced Patterns and Applications. Hershey, PA: IGI Global, 2010. https://doi.org/10.4018/978-1-60566-124-7.ch006

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Abstract

This chapter continues an analysis of the degeneracy of the vertebrate mitochondrial genetic code in the matrix form of its presentation, which possesses the symmetrical black-and-white mosaic. Taking into account a symmetry breakdown in molecular compositions of the four letters of the genetic alphabet, the connection of this matrix form of the genetic code with a Hadamard (8x8)-matrix is discovered. Hadamard matrices are one of the most famous and the most important kinds of matrices in the theory of discrete signals processing and in spectral analysis. The special U-algorithm of transformation of the symbolic genetic matrix [C A; U G](3) into the appropriate Hadamard matrix is demonstrated. This algorithm is based on the molecular parameters of the letters A, C, G, U/T of the genetic alphabet. In addition, the analogical relations is shown between Hadamard matrices and other symmetrical forms of genetic matrices, which are produced from the symmetrical genomatrix [C A; U G](3) by permutations of positions inside triplets. Many new questions arise due to the described fact of the connection of the genetic matrices with Hadamard matrices. Some of them are discussed here, including questions about an importance of amino-group NH2 in molecular-genetic systems, and about possible relations with the theory of quantum computers, where Hadamard gates are utilized. A new possible answer is proposed to the fundamental question concerning reasons for the existence of four letters in the genetic alphabet. Some thoughts about cyclic codes and a principle of molecular economy in genetic informatics are presented as well.

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