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1
Content available remote BCK-codes Based on a Parity Check Matrix
Keshavarzian Nazanin, Borumand Saeid Arsham, Tehranian Abolfazl
Fundamenta Informaticae
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2020
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Vol. 174, nr 2
137--165
EN
Hamming codes are of primary concern in information theory and its applications. Despite a number of researches that have been conducted on such codes and their characterizations, dealing with the properties of previously introduced codes in a BCK-algebraic framework has not been considered in earlier works. This paper investigates a code constructed based on BCK-algebraic models and proposes an algorithm corresponding to the presented code. It is noticeable that the suggested rendered algorithm is also established on the basis of the elements of a BCK-algebra. In fact, both the Hamming distance and dimension, associated with the presented code, can be estimated through a BCK-algebra structure due to the mechanism of its algorithm which is heavily dependent on the parity check matrix. In addition, the way in which the codes are designed contributes substantially to classification of them and to extract greater number of their attributes compared to the previous works. The highlight of the proposed method is that the number of atoms of the BCK-algebra plays a key role in calculation of the Hamming distance and dimension of these codes. Moreover, the obtained codes possess specified and recognizable Hamming distance which are essential in performing error-correcting, error-detecting and decoding tasks.
2
Content available remote The variety of all commutative BCK-algebras is generated by its finite members as a quasivariety
Pałasiński M.
Demonstratio Mathematica
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2012
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Vol. 45, nr 3
495-518
EN
We prove the result announced by the title as well as some of its consequences.
3
Content available remote On BG-algebras
Kim C., Kim H.
Demonstratio Mathematica
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2008
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Vol. 41, nr 3
497-505
EN
In this paper we introduce the notion of BG-algebras which is a generalization of BG-algebras. We construct a BG-algebra from a non-empty set, which is non-group-derived. Moreover, using the notion of normal subalgebra, we obtain several isomorphism theorems of BG-algebra and related properties.
4
Content available remote When is a BCC-algebra equivalent to an MV-algebra?
Chajda I., Halas R., Kuhr J.
Demonstratio Mathematica
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2007
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Vol. 40, nr 4
759-768
EN
The aim of this paper is to characterize BCC-algebras which are term equivalent to MV-algebras. It turns out that they arę just the bounded commutative BCC-algebras. Purther, we characterize congruence kernels as deductive systems. The explicit description of a principal deductive system enables us to prove that every subdirectly irreducible bounded commutatwe BCC-algebra is a chain (with respect to the induced order) .
5
Content available remote Some examples of involutory BCK-algebras
Huang Y.
Demonstratio Mathematica
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2005
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Vol. 38, nr 4
793--798
EN
K. Iseki raised some unsolved problems on BCK-algebras in 1979. One of them is as follows: Is there a non-commutative BCK-algebra satisfying NNx = x? By giving some examples of such algebras, A. Grzaslewicz definitely answered this problem in 1980. Based on Grzaslewicz's work, we give some further examples in this paper.
6
Content available remote Irreducible ideals in BCI-algebras
Huang Y.
Demonstratio Mathematica
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2004
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Vol. 37, nr 1
2--8
EN
In this paper, we show some results of irreducible ideals in BCI-algebras, including that every proper ideal of a BCK-algebra can be decomposed as the intersection of all minimal irreducible ideals associated with it, etc.
7
Content available remote Fuzzy QA-ideals in weak BCC-algebras
Łyczkowska A.
Demonstratio Mathematica
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2001
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Vol. 34, nr 3
513-524
EN
The purpose of this paper is description of properties of QA-ideals and fuzzy QA-ideals in weak BCC-algebras.
8
Content available remote Notes on BCK-algebraa with condition (s)
Huang Y.
Demonstratio Mathematica
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2000
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Vol. 33, nr 3
452-457
EN
Some further properties related to BCK-algebras with the condition (S) are obtained. The main results are as follows: (i) If a commutative BCK-algebra X is a lattice with respect to the BCK-ordering <, then X need not be with the condition (S); (ii) A positive implicative BCK-algebra X with the condition (S) may not be a lattice with respect to <, moreover, if (X; <) is a lattice, it must be a distributive lattice; (iii) Each involutory BCK-algebra is with the condition (S).
9
Content available remote On representations of commutative BCK-algebras
Dvurecenskij A., Graziano M.
Demonstratio Mathematica
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1999
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Vol. 32, nr 2
227-246
EN
We introduce the relative cancellation property for commutative BCK-algebras and we study the problem of embedding of commutative BCK-algebras into Abelian lattice ordered groups. We show that if a BCK-algebra is not directed upwards, then we cannot use the method of Wyler and Baer. Anyway, supposing either union property or unitary extendibility, we can present the embedding of such a BCK-algebra into the positive cone of an Abelian lattice ordered group with universal property. Finally, some interesting examples are presented.
10
Content available remote On commutative residual ponoids
Meng J.
Demonstratio Mathematica
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1998
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Vol. 31, nr 1
11-17
EN
In the present paper we prove the following r
11
Content available remote Fuzzy prime and fuzzy irreducible BCK-filters in BCK-algebras
Jun Y., Zhang F.
Demonstratio Mathematica
|
1998
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Vol. 31, nr 3
519-527
EN
In this paper we discuss the fuzzification of prime and irreducible BCK-filters in BCK-algebras, and invesigate its properties.
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