Error Correction for Check Digit Systems over p-Groups and Applications to DNA Sequences
Statistical analysis shows that the most common errors in the transmission of information consist of single errors and transposition errors. Error detection and correction methods are often desired, particularly when the accuracy of information is of crucial importance. Inspired by a check digit sys...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/2/211 |
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| author | Louis Beaugris |
| author_facet | Louis Beaugris |
| author_sort | Louis Beaugris |
| collection | DOAJ |
| description | Statistical analysis shows that the most common errors in the transmission of information consist of single errors and transposition errors. Error detection and correction methods are often desired, particularly when the accuracy of information is of crucial importance. Inspired by a check digit system constructed from the companion matrix of a primitive polynomial over the integers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula> and that focused on error detection, this work develops error-correction formulas for single errors and transposition errors for that check digit scheme. We also propose an application to DNA sequences. |
| format | Article |
| id | doaj-art-eb4cf91c76124c849b443f507a2a802f |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-eb4cf91c76124c849b443f507a2a802f2025-01-24T13:39:45ZengMDPI AGMathematics2227-73902025-01-0113221110.3390/math13020211Error Correction for Check Digit Systems over p-Groups and Applications to DNA SequencesLouis Beaugris0Department of Mathematical Sciences, Kean University, 1000 Morris Avenue, Union, NJ 07083, USAStatistical analysis shows that the most common errors in the transmission of information consist of single errors and transposition errors. Error detection and correction methods are often desired, particularly when the accuracy of information is of crucial importance. Inspired by a check digit system constructed from the companion matrix of a primitive polynomial over the integers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula> and that focused on error detection, this work develops error-correction formulas for single errors and transposition errors for that check digit scheme. We also propose an application to DNA sequences.https://www.mdpi.com/2227-7390/13/2/211error correctioncheck digitcompanion matrixGalois field |
| spellingShingle | Louis Beaugris Error Correction for Check Digit Systems over p-Groups and Applications to DNA Sequences Mathematics error correction check digit companion matrix Galois field |
| title | Error Correction for Check Digit Systems over p-Groups and Applications to DNA Sequences |
| title_full | Error Correction for Check Digit Systems over p-Groups and Applications to DNA Sequences |
| title_fullStr | Error Correction for Check Digit Systems over p-Groups and Applications to DNA Sequences |
| title_full_unstemmed | Error Correction for Check Digit Systems over p-Groups and Applications to DNA Sequences |
| title_short | Error Correction for Check Digit Systems over p-Groups and Applications to DNA Sequences |
| title_sort | error correction for check digit systems over p groups and applications to dna sequences |
| topic | error correction check digit companion matrix Galois field |
| url | https://www.mdpi.com/2227-7390/13/2/211 |
| work_keys_str_mv | AT louisbeaugris errorcorrectionforcheckdigitsystemsoverpgroupsandapplicationstodnasequences |