BCK-algebras arising from block codes

Flaut, Cristina

doi:10.3233/ifs-141469

Cited by 14 publications

(7 citation statements)

References 9 publications

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“…Let C be a binary block code with n codewords of length m. From Proposition 3.8 and Theorem 3.9 from (Flaut, 2015), we find a BCK-algebra X such that the obtained binary block-code V X contains the binary block-code C as a subset. In the following, we briefly present this procedure.…”

Section: Resultsmentioning

confidence: 99%

“…is a non-commutative and a non-implicative algebra. (see (Diego,1966) and (Flaut, 2015)) Definition 2.3. A Hilbert algebra is a triplet (H, * , 1) in which H is a non-empty set, " * " a binary operation on H and 1 ∈ H is a fixed element such that the following relations hold, for all x, y, z ∈ H:…”

Section: Preliminariesmentioning

confidence: 99%

“…Conclusions. In the papers (Jun, Song, 2011), (Flaut, 2015), (Borumand Saeid, Fatemidokht, Flaut, Kuchaki Rafsanjani, 2015), some connections between BCK-algebras and binary block codes were described. In this paper we make some connections between Hilbert algebras and binary block codes via BCK-algebra defined by relation (2.1).…”

mentioning

confidence: 99%

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Some Connections Between Binary Block Codes and Hilbert Algebras

Flaut

2016

Recent Trends in Social Systems: Quantitative Theories and Quantitative Models

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In this paper, we will study some connections between Hilbert algebras and binary block-codes.With these codes, we can eassy obtain orders which determine suplimentary properties on these algebras. We will try to emphasize how, using binary block-codes, we can provide examples of classes of Hilbert algebras with some properties, in our case, classes of semisimple Hilbert algebras and classes of local Hilbert algebras.

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Section: Resultsmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

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Some Connections Between Binary Block Codes and Hilbert Algebras

Flaut

2016

Recent Trends in Social Systems: Quantitative Theories and Quantitative Models

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“…At the end of the paper, they raised the question of whether the converse of this statement was also true. In [36] an answer was given to this question: under some circumstances, the converse is also true. Therefore we can associate a finite BCK algebra to a finite binary block code.…”

Section: Codes and Bck-algebrasmentioning

confidence: 99%

From Old Ciphers to Modern Communications

Flaut

Hošková-Mayerová³

et al. 2019

AiMT

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The security of the information transmitted, irrespective of the era and the channel selected, has always been one of the main concerns of those using various communication systems. This is particularly the case nowadays, when the Internet has made the mass distribution of any kind of information possible. Codes can be used to transmit data through various noisy channels and any errors that might occur can be corrected; it is therefore very important to design gappropriate codes with adequate parameters. This survey briefly outlines the evolution of the ways in which information has been collected, transmitted and used from the past to the present.

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“…For other conections of different types of algebras with codes, the reader is referred to (Flaut, 2015).…”

Section: Introductionmentioning

confidence: 99%