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Title:The Structure of the Block Code Generated by a BL-Algebra
Authors:Bordbar, Hashem (Author)
Files:.pdf mathematics-10-00692.pdf (261,87 KB)
 
Language:English
Work type:Not categorized (r6)
Tipology:1.01 - Original Scientific Article
Organization:UNG - University of Nova Gorica
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.
Keywords:BL-function, BL-code, binary linear block codes, coding theory, BL-algebra
Year of publishing:2022
Number of pages:11
Numbering:10, 5
COBISS_ID:99906819 Link is opened in a new window
URN:URN:SI:UNG:REP:JPBMBSBD
DOI:https://doi.org/10.3390/math10050692 Link is opened in a new window
License:CC BY-NC-ND 4.0
This work is available under this license: Creative Commons Attribution Non-Commercial No Derivatives 4.0 International
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Title:Mathematics(MDPI)
ISSN:2227-7390
Year of publishing:2022

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