BCK codes

Bordbar, Hashem

doi:10.1007/s43674-021-00018-4

Cited by 3 publications

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Jun and Song applied coding theory to these algebras in [14]. Recently, binary block codes produced by different ordered algebraic structures have been investigated by many mathematicians in [1], [2], [10], [11], [12], [15], [16], [17].…”

Section: Introductionmentioning

confidence: 99%

Codes based on basic algebras

Yılmaz

2022

Preprint

View full text Add to dashboard Cite

In this article, we consider basic algebra, a common generalization of an MV-algebra (an algebraic counterpart of the Lukasiewicz many-valued propositional logic) and an orthomodular lattice (an algebraic counterpart of the logic of quantum mechanics). We get some results regarding b-functions and b-subsets by giving the concept of basic-function on a nonempty set V . We also build a basic code W and explore a new order of it. Finally, we prove that the corresponding orders of the basic algebra B and the basic code W generated by B are the same.

show abstract

Section: Introductionmentioning

confidence: 99%

Codes based on basic algebras

Yılmaz

2022

Preprint

View full text Add to dashboard Cite

show abstract

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

Bordbar

2022

Mathematics

View full text Add to dashboard Cite

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.

show abstract

Ordered algebraic structure in a linear code

Bordbar

2024

AMC

View full text Add to dashboard Cite

BCK codes

Cited by 3 publications

References 15 publications

Codes based on basic algebras

Codes based on basic algebras

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

Ordered algebraic structure in a linear code

Contact Info

Product

Resources

About