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

Author

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  • Hashem Bordbar

    (Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia)

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.

Suggested Citation

  • Hashem Bordbar, 2022. "The Structure of the Block Code Generated by a BL -Algebra," Mathematics, MDPI, vol. 10(5), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:692-:d:756473
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    Cited by:

    1. Irina Cristea & Hashem Bordbar, 2023. "Preface to the Special Issue “Algebraic Structures and Graph Theory”," Mathematics, MDPI, vol. 11(15), pages 1-4, July.

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