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

**Hashem Bordbar**

Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia; hashem.bordbar@ung.si; Tel.: +386-070-614-786

**Abstract:** 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.

**Keywords:** *BL*-function; *BL*-code; binary linear block codes; coding theory; *BL*-algebra
