The Structure of the Block Code Generated by a BL-Algebra
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.
2022
2022-03-07 10:48:23
1033
BL-function,BL-code,binary linear block codes,coding theory,BL-algebra
r6
Hashem
Bordbar
70
COBISS_ID
3
99906819
URN
14
URN:SI:UNG:REP:JPBMBSBD
DOI
15
https://doi.org/10.3390/math10050692
mathematics-10-00692.pdf
268150
Predstavitvena datoteka
2022-03-07 10:49:27
0
Izvorni URL
2022-03-07 10:48:24