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The Structure of the Block Code Generated by a BL -Algebra.
- Source :
- Mathematics (2227-7390); Mar2022, Vol. 10 Issue 5, p692, 1p
- Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- BLOCK codes
CODING theory
LINEAR codes
ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 10
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 155706951
- Full Text :
- https://doi.org/10.3390/math10050692