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.
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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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Balonin, N.A., Sergeev, M.B., Petoukhov, S.V. (2020). Development of Matrix Methods for Genetic Analysis and Noise-Immune Coding. In: Hu, Z., Petoukhov, S., He, M. (eds) Advances in Artificial Systems for Medicine and Education III. AIMEE 2019. Advances in Intelligent Systems and Computing, vol 1126. Springer, Cham. https://doi.org/10.1007/978-3-030-39162-1_4
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