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Development of Matrix Methods for Genetic Analysis and Noise-Immune Coding

  • Nikolay A. BaloninEmail author
  • Mikhail B. Sergeev
  • Sergey V. Petoukhov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1126)

Abstract

The article discusses new methods of studying and using Hadamard matrices. This class of matrices is commonly used in developing AI systems, noise-immune coding of data and simulation of bioinformational entities. The relations between Hadamard matrices and hyper-complex numbers are discussed. A special attention is given to the new method of pre-orthogonal sequences for building multi-block Hadamard matrices of large orders. This method, due to its mathematical characteristics, should also be useful in modeling the noise-immunity features of genetic coding.

Keywords

Hadamard matrices Cyclic shifts Noise immunity Bioinformatics 

Notes

Acknowledgement

The authors express their gratitude for long-standing collaboration and support to professors Jennifer Seberry and Dragomir Ðoković. In technical work with the manuscript and references, T.V. Balonina was very helpful (find a more complete list of works on http://mathscinet.ru/tamara).

The work has been carried out with the support of Ministry of Education and Science of the Russian Federation for research within the development part of the scientific governmental task #2.2200.2017/4.6.

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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Nikolay A. Balonin
    • 1
    Email author
  • Mikhail B. Sergeev
    • 1
  • Sergey V. Petoukhov
    • 2
  1. 1.Saint Petersburg State University of Aerospace InstrumentationSt. PetersburgRussian Federation
  2. 2.Mechanical Engineering Research Institute of the Russian Academy of SciencesMoscowRussian Federation

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