The Structure of the Block Code Generated by a BL -Algebra

Hashem Bordbar
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Hashem Bordbar: Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia

Mathematics, 2022, vol. 10, issue 5, 1-11

Abstract: Inspired by the concept of B L -algebra as an important part of the ordered algebra, in this paper we investigate the binary block code generated by an arbitrary B L -algebra and study related properties. For this goal, we initiate the study of the B L -function on a nonempty set P based on B L -algebra L , and by using that, l -functions and l -subsets are introduced for the arbitrary element l of a B L -algebra. In addition, by the mean of the l -functions and l -subsets, an equivalence relation on the B L -algebra L is introduced, and using that, the structure of the code generated by an arbitrary B L -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 B L -algebra L , and show that the structures of the B L -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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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