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Article | Open Access

Binary Fuzzy Codes and Some Properties of Hamming Distance of Fuzzy Codes

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
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Abstract

In this paper, we discussed binary fuzzy codes over a vector space F2n by relating classical codes with the probability of a binary symmetric channel (BSC) for receiving a sent codeword correctly. We used the weight of error patterns between a received word and the possible sent codewords to define fuzzy words over n-dimensional vector space F2n, and used it to define binary fuzzy codes. We also added some properties of Hamming distance of binary fuzzy codes, and the bounds of a Hamming distance of binary fuzzy codes for p=1/r, where r⩾3, and r∈Z+, are determined. Finding Hamming distance of binary fuzzy codes is used for decoding sent messages on a BSC.

Keywords

classical codesbinary fuzzy codesfuzzy space and Hamming distance

References

[1]

L. A. Zadeh, Fuzzy sets, Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.
Crossref Google Scholar
[2]

C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J., vol. 27, no. 3, pp. 379–423, 1948.
Crossref Google Scholar
[3]
C. E. Shannon, Certain results in coding theory for noisy channels, Inf. Control, vol. 1, no. 1, pp. 6–25, 1957.
Crossref
[4]

R. W. Hamming, Error detecting and error correcting codes, Bell Syst. Tech. J., vol. 29, no. 2, pp. 147–160, 1950.
Crossref Google Scholar
[5]

R. C. Bose and D. K. Ray-Chaudhuri, On a class of error correcting binary group codes, Inf. Control, vol. 3, no. 1, pp. 68–79, 1960.
Crossref Google Scholar
[6]

D. E. Muller, Application of Boolean algebra to switching circuit design and to error detection, Trans. I. R. E. Prof. Group Electron. Comput., vol. EC-3, no. 3, pp. 6–12, 1954.
Crossref Google Scholar
[7]
I. S. Reed, A class of multiple-error-correcting codes and the decoding scheme, Technical Report, Massachusetts Inst of Tech Lexington Lincoln Lab AD0025814, Lexington, MA, USA, 1953.
[8]

I. S. Reed and G. Solomon, Polynomial codes over certain finite fields, J. Soc. Indust. Appl. Math., vol. 8, no. 2, pp. 300–304, 1960.
Crossref Google Scholar
[9]

P. A. von Kaenel, Fuzzy codes and distance properties, Fuzzy Sets Syst., vol. 8, no. 2, pp. 199–204, 1982.
Crossref Google Scholar
[10]
S. Ling and C. Xing, Coding Theory: A First Course. Cambridge, UK: Cambridge University Press, 2004.
Crossref
[11]

S. A. Tsafack, S. Ndjeya, L. Strüngmann, and C. Lele, Fuzzy linear codes, Fuzzy Information and Engineering, vol. 10, no. 4, pp. 418–434, 2018.
Crossref Google Scholar
[12]

B. Amudhambigai and A. Neeraja, A new view on fuzzy codes and its application, Jordan J. Math. Stat., vol. 12, no. 4, pp. 455–471, 2019.
Google Scholar
[13]

A. Ozkan and E. M. Ozkan, A different approach to coding theory, J. Appl. Sci., vol. 2, no. 11, pp. 1032–1033, 2002.
Crossref Google Scholar
[14]

P. Lubczonok, Fuzzy vector spaces, Fuzzy Sets Syst., vol. 38, no. 3, pp. 329–343, 1990.
Crossref Google Scholar
[15]

R. Lowen, Convex fuzzy sets, Fuzzy Sets Syst., vol. 3, no. 3, pp. 291–310, 1980.
Crossref Google Scholar
Fuzzy Information and Engineering
Volume 15 Issue 1,
March 2023
Pages 26-35
DOI: 10.26599/FIE.2023.9270003
Cite this article:
Gereme MM, Demamu J, Alaba BA. Binary Fuzzy Codes and Some Properties of Hamming Distance of Fuzzy Codes. Fuzzy Information and Engineering, 2023, 15(1): 26-35. https://doi.org/10.26599/FIE.2023.9270003

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Received: 13 September 2022
Revised: 20 October 2022
Accepted: 29 October 2022
Published: 06 April 2023
© The Author(s) 2023. Published by Tsinghua University Press.

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