| Title: | The Structure of the Block Code Generated by a BL-Algebra |
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| Authors: | ID Bordbar, Hashem, University of Nova Gorica (Author) |
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| Files: |  mathematics-10-00692.pdf (261,87 KB)
MD5: C0EDDEF72E2F85BF1A9E3594D726A0C1
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | UNG - University of Nova Gorica
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| Abstract: | Inspired by the concept of BL-algebra as an important part of the ordered algebra, in this paper we investigate the binary block code generated by an arbitrary BL-algebra and study related properties. For this goal, we initiate the study of the BL-function on a nonempty set P based on BL-algebra L, and by using that, l-functions and l-subsets are introduced for the arbitrary element l of a BL-algebra. In addition, by the mean of the l-functions and l-subsets, an equivalence relation on the BL-algebra L is introduced, and using that, the structure of the code generated by an arbitrary BL-algebra is considered. Some related properties (such as the length and the linearity) of the generated code and examples are provided. Moreover, as the main result, we define a new order on the generated code C based on the BL-algebra L, and show that the structures of the BL-algebra with its order and the correspondence generated code with the defined order are the same. |
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| Keywords: | BL-function, BL-code, binary linear block codes, coding theory, BL-algebra |
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| Publication version: | Version of Record |
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| Year of publishing: | 2022 |
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| Number of pages: | 11 |
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| Numbering: | 5, 10 |
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| PID: | 20.500.12556/RUNG-7225  |
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| COBISS.SI-ID: | 99906819 |
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| DOI: | https://doi.org/10.3390/math10050692 |
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| NUK URN: | URN:SI:UNG:REP:JPBMBSBD |
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| Publication date in RUNG: | 07.03.2022 |
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| Views: | 2318 |
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| Downloads: | 54 |
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