Identification of proteins by the use of Chinese remainder theorem codes over finite commutative rings

In recent works, error-correcting codes have been applied for modeling the reliability in the transmission of genetic information, wherein DNA and RNA sequences and proteins are considered as codewords of cyclic codes. In the case of proteins, cyclic codes over alphabets Z 20 ≃ Z 4 ⊕ Z 5 and F 4 ⊕ Z...

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Bibliographic Details
Published in:Computational & applied mathematics 2022-09, Vol.41 (6), Article 231
Main Authors: Duarte-González, Mario E., Bastos, Gustavo Terra, Palazzo, Reginaldo
Format: Article
Language:English
Subjects:
Algorithms
Alphabets
Applications of Mathematics
Applied physics
BCH codes
Binary system
Codes
Computational mathematics
Computational Mathematics and Numerical Analysis
Error correcting codes
Error correction
Gene sequencing
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Proteins
Rings (mathematics)
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Summary:In recent works, error-correcting codes have been applied for modeling the reliability in the transmission of genetic information, wherein DNA and RNA sequences and proteins are considered as codewords of cyclic codes. In the case of proteins, cyclic codes over alphabets Z 20 ≃ Z 4 ⊕ Z 5 and F 4 ⊕ Z 5 have been constructed by juxtaposing BCH codes; however, such codes are restrictive in length, and therefore, several proteins cannot be analyzed. To overcome the length constraints, in this work, we propose a new procedure for constructing codes over finite commutative rings with identity. The proposed construction is a reinterpretation of the Chinese product code construction and is based on the decomposition of a commutative ring as a direct sum of local rings and on the juxtaposition of repetition codes with not necessarily equal lengths. For the constructed codes, we derive its parameters, a minimal spanning set and the conditions to be a free submodule and a cyclic code. We also introduce two algorithms, one for checking whether a sequence belongs to the resulting code, and the other for correcting random and burst errors. Using the proposed procedure, we design codes over alphabets Z 20 ≃ Z 4 ⊕ Z 5 and F 4 ⊕ Z 5 , and identify proteins as codewords of such codes. Therefore, to the best of our knowledge, for the first time a mathematical structure associated with such a class of proteins is identified.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-022-01767-9