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Fuzzy Information and Engineering 2023, 15(4): 335-346 https://doi.org/10.26599/FIE.2023.9270024
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Updates on Properties of Hamming Distance of Binary Fuzzy Codes over Fuzzy Vector Spaces and Their Application in Decoding Process

Show Author's Information Mezgebu Manmekto Gereme1,2( ),  Jejaw Demamu1,2,  Berhanu Assaye Alaba1
Department of Mathematics, Bahir Dar University, Bahir Dar 6000, Ethiopia
Department of Mathematics, Debark University, Debark 6200, Ethiopia
Keywords:
Hamming distance, classical codes, binary fuzzy codes, fuzzy vector space, decoding fuzzy codes
Cite this article:
Gereme MM, Demamu J, Alaba BA. Updates on Properties of Hamming Distance of Binary Fuzzy Codes over Fuzzy Vector Spaces and Their Application in Decoding Process. Fuzzy Information and Engineering, 2023, 15(4): 335-346. https://doi.org/10.26599/FIE.2023.9270024
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Abstract Full text About this article

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.


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About this article

Updates on Properties of Hamming Distance of Binary Fuzzy Codes over Fuzzy Vector Spaces and Their Application in Decoding Process

Show Author's information Mezgebu Manmekto Gereme1,2( ), Jejaw Demamu1,2, Berhanu Assaye Alaba1
Department of Mathematics, Bahir Dar University, Bahir Dar 6000, Ethiopia
Department of Mathematics, Debark University, Debark 6200, Ethiopia

Abstract

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.

Keywords: Hamming distance, classical codes, binary fuzzy codes, fuzzy vector space, decoding fuzzy codes

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Received: 05 May 2023
Revised: 20 June 2023
Accepted: 30 October 2023
Published: 02 January 2024
Issue date: December 2023

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© The Author(s) 2023. Published by Tsinghua University Press.

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This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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