ǂThe ǂstructure of the block code generated by a BL-algebra

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;

Data

Language:	English
Year of publishing:	2022
Typology:	1.01 - Original Scientific Article
Organization:	UNG - University of Nova Gorica
UDC:	510.3
COBISS:	99906819
ISSN:	2227-7390
Views:	796
Downloads:	36
Average score:	0 (0 votes)
Metadata:

Other data

URN:	URN:SI:UNG
Type (COBISS):	Not categorized
Pages:	str. 1-11
Volume:	ǂVol. ǂ10
Issue:	ǂiss. ǂ5
Chronology:	2022
DOI:	10.3390/math10050692
ID:	14696415