期刊
MATHEMATICS
卷 10, 期 5, 页码 -出版社
MDPI
DOI: 10.3390/math10050692
关键词
BL-function; BL-code; binary linear block codes; coding theory; BL-algebra
类别
This paper investigates the binary block code generated by an arbitrary BL-algebra and its properties. It introduces the concept of BL-functions and BL-subsets to study the structure of the BL-algebra and defines a new order on the generated code.
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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