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

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. [ABSTRACT FROM AUTHOR]