The degeneracy of the genetic code and Hadamard matrices

Abstract

The matrix form of the presentation of the genetic code is described as the cognitive form to analyze structures of the genetic code. A similar matrix form is utilized in the theory of signal processing. The Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C A; U G], where C, A, U, G are the letters of the genetic alphabet. This matrix in the third Kronecker power is the (8*8)-matrix, which contains 64 triplets. Peculiarities of the degeneracy of the vertebrate mitochondria genetic code are reflected in the symmetrical black-and-white mosaic of this genetic (8*8)-matrix. This mosaic matrix is connected algorithmically with Hadamard matrices unexpectedly, which are famous in the theory of signal processing, spectral analysis, quantum mechanics and quantum computers. A special decomposition of numeric genetic matrices reveals their close relations with a family of 8-dimensional hypercomplex numbers (not Cayley's octonions). Some hypothesis and thoughts are formulated on the basis of these phenomenological facts.

26 pages; 21 figures; added materials and references

References in corpus (8)

• A p-Adic Model of DNA Sequence and Genetic Code
• Genetic code on the dyadic plane
• p-Adic Modelling of the Genome and the Genetic Code
• Matrix genetics, part 2: the degeneracy of the genetic code and the octave algebra with two quasi-real units (the genetic octave Yin-Yang-algebra)
• Matrix genetics, part 1: permutations of positions in triplets and symmetries of genetic matrices
• Matrix genetics, part 3: the evolution of the genetic code from the viewpoint of the genetic octave Yin-Yang-algebra
• Octonionic Cayley Spinors and E6
• Matrix genetics, part 4: cyclic changes of the genetic 8-dimensional Yin-Yang-algebras and the algebraic models of physiological cycles

Cited by in corpus (8)

• The rules of long DNA-sequences and tetra-groups of oligonucleotides
• Matrix genetics, part 2: the degeneracy of the genetic code and the octave algebra with two quasi-real units (the genetic octave Yin-Yang-algebra)
• The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts
• Matrix genetics, part 1: permutations of positions in triplets and symmetries of genetic matrices
• The genetic code, algebra of projection operators and problems of inherited biological ensembles
• Matrix genetics, part 3: the evolution of the genetic code from the viewpoint of the genetic octave Yin-Yang-algebra
• Matrix genetics, part 4: cyclic changes of the genetic 8-dimensional Yin-Yang-algebras and the algebraic models of physiological cycles
• Dyadic groups, dyadic trees and symmetries in long nucleotide sequences