Wajsberg algebras arising from binary block codes

Flaut, Cristina; Vasile, Radu

doi:10.1007/s00500-019-04653-5

Cited by 5 publications

(7 citation statements)

References 9 publications

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“…In [1], [4] was presented classification of MV-algebras by using different algorithms. In [5] was presented an application of these algebras in Coding Theory. In the following, by using examples from [4], Sections 4.1-4.3 and the above Remark 1.6, ii), which give an alternative method to characterize MV-algebras and, as a consequence, Boolean algebras, we will give some examples of MV-algebras and Boolean algebras.…”

Section: Examplesmentioning

confidence: 99%

“…In this section we will denote Boolean algebras of order 2 k , k ≥ 1, with B 2 k . In [5], to an MV-algebra and to a Wajsberg algebra were associated binary block codes and, in some circumstances, it was proved that the converse is also true. Using some of these ideas, to algebra B 2 k+1 we will associate a binary block code and we will prove that the converse of this statement is also true, namely to such a binary block code a Boolean algebra B 2 k+1 can be associated.…”

Section: Binary Block Codes Associated To a Boolean Algebramentioning

confidence: 99%

“…In the last decades, numerous papers have been devoted to the study of the properties and the applications of MV-algebras, Wajsberg algebras and Boolean algebras. Some applications of these algebras were provided in [5], where was presented an algorithm which can built Wajsberg algebras starting from a binary block codes.…”

Section: Introductionmentioning

confidence: 99%

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Some applications of idempotent elements in MV algebras

Flaut¹

2022

CJM

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"In this paper we provide some properties and applications of MV-algebras. We prove that a Fibonacci stationary sequence in an MV-algebra gives us an idempotent element. Moreover, taking into account of the representation of a finite MV-algebra, by using Boolean elements of this algebra, we prove that a Fibonacci sequence in an MV-algebra is always stationary. This result is interesting comparing with the behavior of such a sequence on the group $\left( \mathbb{Z}% _{n},+\right) $, where the Fibonacci sequences are periodic, with the period given by the Pisano period. We also give some examples of finite MV-algebras and the number of their idempotent elements. As an application in Coding Theory, to a Boolean algebra it is attached a binary block code and it is proved that, under some conditions, the converse is also true."

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Section: Examplesmentioning

confidence: 99%

Section: Binary Block Codes Associated To a Boolean Algebramentioning

confidence: 99%

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Some applications of idempotent elements in MV algebras

Flaut¹

2022

CJM

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“…e binary block codes associated to UP-algebras were discussed by Moin et al [13]. Wajsberg algebras arising from binary block codes were studied by Flaut and Vasile [14].…”

Section: Introductionmentioning

confidence: 99%

Generalized Cut Functions and n‐Ary Block Codes on UP‐Algebras

Koam

Haider

Ansari

2022

Journal of Mathematics

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In this paper, the work is comprised of n -ary block codes for UP-algebras and their interrelated properties. n -ary block codes for a known UP-algebra is constructed and further it is shown that for each n -ary block code U , it is easy to associate a UP-algebra U in such a way that the newly constructed n -ary block codes generated by U , i.e., U x , contain the code U as a subset. We define a UP-algebra valued function on a set say X , then we prove that for every n -ary block-code U , a generalized UP-valued cut function exists that determines U . We have also proved that the UP-algebras associated to an n -ary block code are not unique up to isomorphism.

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“…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

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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.

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Wajsberg algebras arising from binary block codes

Cited by 5 publications

References 9 publications

Some applications of idempotent elements in MV algebras

Some applications of idempotent elements in MV algebras

Generalized Cut Functions and n‐Ary Block Codes on UP‐Algebras

Codes based on basic algebras

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