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

Povzetek

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.

Ključne besede

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

Podatki

Jezik:	Angleški jezik
Leto izida:	2022
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UNG - Univerza v Novi Gorici
UDK:	510.3
COBISS:	99906819
ISSN:	2227-7390
Št. ogledov:	796
Št. prenosov:	36
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

URN:	URN:SI:UNG
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	str. 1-11
Letnik:	ǂVol. ǂ10
Zvezek:	ǂiss. ǂ5
Čas izdaje:	2022
DOI:	10.3390/math10050692
ID:	14696415