Updates on Properties of Hamming Distance of Binary Fuzzy Codes over Fuzzy Vector Spaces and Their Application in Decoding Process
In this paper, we used the definition of fuzzy vector spaces and fuzzy subsets in combination in order to define fuzzy codes over a fuzzy vector space. We found that the combined definitions did not satisfy the definition of fuzzy vector spaces over a Galois field F2, and gave the conditions in whic...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2023-12-01
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| Series: | Fuzzy Information and Engineering |
| Subjects: | |
| Online Access: | https://www.sciopen.com/article/10.26599/FIE.2023.9270024 |
| _version_ | 1797354893772587008 |
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| author | Mezgebu Manmekto Gereme Jejaw Demamu Berhanu Assaye Alaba |
| author_facet | Mezgebu Manmekto Gereme Jejaw Demamu Berhanu Assaye Alaba |
| author_sort | Mezgebu Manmekto Gereme |
| collection | DOAJ |
| description | In this paper, we used the definition of fuzzy vector spaces and fuzzy subsets in combination in order to define fuzzy codes over a fuzzy vector space. We found that the combined definitions did not satisfy the definition of fuzzy vector spaces over a Galois field F2, and gave the conditions in which the combined definitions hold the definition of fuzzy vector spaces in order to define binary fuzzy codes. By defining binary fuzzy codes over fuzzy vector space in relation to the probability of binary symmetric channels (BSC) sending a codeword incorrectly and the weight of error pattern between codewords, we updated properties of Hamming distance of binary fuzzy codes over fuzzy vector space. From the updated properties, we found that the properties of Hamming distance stated over a vector space also satisfy in binary fuzzy codes defined over a fuzzy vector space. Furthermore, we found some interesting results on the decoding of fuzzy codewords sent over a BSC using minimum non-zero Hamming distance of binary fuzzy codes. |
| first_indexed | 2024-03-08T13:56:22Z |
| format | Article |
| id | doaj.art-b1c869ab1f734e39b2503c1e8bc6db7a |
| institution | Directory Open Access Journal |
| issn | 1616-8658 1616-8666 |
| language | English |
| last_indexed | 2024-03-08T13:56:22Z |
| publishDate | 2023-12-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj.art-b1c869ab1f734e39b2503c1e8bc6db7a2024-01-15T14:15:17ZengTsinghua University PressFuzzy Information and Engineering1616-86581616-86662023-12-0115433534610.26599/FIE.2023.9270024Updates on Properties of Hamming Distance of Binary Fuzzy Codes over Fuzzy Vector Spaces and Their Application in Decoding ProcessMezgebu Manmekto Gereme0Jejaw Demamu1Berhanu Assaye Alaba2Department of Mathematics, Bahir Dar University, Bahir Dar 6000, EthiopiaDepartment of Mathematics, Bahir Dar University, Bahir Dar 6000, EthiopiaDepartment of Mathematics, Bahir Dar University, Bahir Dar 6000, EthiopiaIn this paper, we used the definition of fuzzy vector spaces and fuzzy subsets in combination in order to define fuzzy codes over a fuzzy vector space. We found that the combined definitions did not satisfy the definition of fuzzy vector spaces over a Galois field F2, and gave the conditions in which the combined definitions hold the definition of fuzzy vector spaces in order to define binary fuzzy codes. By defining binary fuzzy codes over fuzzy vector space in relation to the probability of binary symmetric channels (BSC) sending a codeword incorrectly and the weight of error pattern between codewords, we updated properties of Hamming distance of binary fuzzy codes over fuzzy vector space. From the updated properties, we found that the properties of Hamming distance stated over a vector space also satisfy in binary fuzzy codes defined over a fuzzy vector space. Furthermore, we found some interesting results on the decoding of fuzzy codewords sent over a BSC using minimum non-zero Hamming distance of binary fuzzy codes.https://www.sciopen.com/article/10.26599/FIE.2023.9270024classical codesbinary fuzzy codesfuzzy vector spacehamming distancedecoding fuzzy codes |
| spellingShingle | Mezgebu Manmekto Gereme Jejaw Demamu Berhanu Assaye Alaba Updates on Properties of Hamming Distance of Binary Fuzzy Codes over Fuzzy Vector Spaces and Their Application in Decoding Process Fuzzy Information and Engineering classical codes binary fuzzy codes fuzzy vector space hamming distance decoding fuzzy codes |
| title | Updates on Properties of Hamming Distance of Binary Fuzzy Codes over Fuzzy Vector Spaces and Their Application in Decoding Process |
| title_full | Updates on Properties of Hamming Distance of Binary Fuzzy Codes over Fuzzy Vector Spaces and Their Application in Decoding Process |
| title_fullStr | Updates on Properties of Hamming Distance of Binary Fuzzy Codes over Fuzzy Vector Spaces and Their Application in Decoding Process |
| title_full_unstemmed | Updates on Properties of Hamming Distance of Binary Fuzzy Codes over Fuzzy Vector Spaces and Their Application in Decoding Process |
| title_short | Updates on Properties of Hamming Distance of Binary Fuzzy Codes over Fuzzy Vector Spaces and Their Application in Decoding Process |
| title_sort | updates on properties of hamming distance of binary fuzzy codes over fuzzy vector spaces and their application in decoding process |
| topic | classical codes binary fuzzy codes fuzzy vector space hamming distance decoding fuzzy codes |
| url | https://www.sciopen.com/article/10.26599/FIE.2023.9270024 |
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