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2. Computational algebra, coding theory and cryptography : theory and applicationsscientific monograph Abstract: This Special Issue explores cutting-edge advancements in computational algebra, coding theory, and cryptography, emphasizing both theoretical foundations and practical applications. Topics covered in this Special Issue include algebraic structures in coding theory, cryptographic protocols, error-correcting codes, and their intersections with mathematical frameworks.
Keywords: algebraic structures, coding theory, cryptography, linear codes, quantum codes, polycyclic codes, self-dual codes, Hermitian codes, quasicyclic codes, codes over rings
Published in RUNG: 03.02.2025; Views: 416; Downloads: 1
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5. SBE-algebras via intuitionistic fuzzy structuresTahsin Oner, Hashem Bordbar, Neelamegarajan Rajesh, Akbar Rezaei, 2024, original scientific article Abstract: The study introduces the concept of intuitionistic fuzzy SBE-subalgebras, ideals, and filters, along with level sets of intuitionistic fuzzy sets within the framework of Sheffer stroke BE-algebras. These concepts are shown to be crucial for understanding the behavior of intuitionistic fuzzy logic in this algebraic structure. The study further establishes a bidirectional relationship between subalgebras, ideals, filters, and their respective level sets on Sheffer stroke BE-algebras, demonstrating that the level set of an intuitionistic fuzzy SBE-subalgebra, ideal, or filter is itself a subalgebra, ideal, or filter on this algebra, and vice versa.
Keywords: BE-algebra, Sheffer stroke BE-algebra, BE-ideal, intuitionistic fuzzy SBE-subalgebra, intuitionistic fuzzy SBE-ideal
Published in RUNG: 06.01.2025; Views: 444; Downloads: 4
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6. Matematika za gospodarski inženiringIrina Elena Cristea, Hashem Bordbar, Alessandro Linzi, 2024, reviewed university, higher education or higher vocational education textbook Keywords: linearna algebra, funkcije, limite, zveznost, diferencialni račun, integrabilnost, funkcije več spremenljivk, diferencialne enačbe
Published in RUNG: 09.12.2024; Views: 624; Downloads: 2
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7. Ordered algebraic structure in a linear codeHashem Bordbar, 2024, original scientific article Abstract: In this article, we initiate an exploration of the algebraic structures
within coding theory. Specifically, we focus on the potential for an ordered al-
gebraic structure, known as a BCI-algebra, within an arbitrary linear code
C. We demonstrate that any binary linear code C of length n, where n is
a positive integer, can be equipped with a BCI-algebra structure between its
codewords. This structure is called BCI-algebra over the code C and denoted
by (BCI)C -algebra. To establish this structure, we define an operation ∗C be-
tween the codewords and investigate its properties. Additionally, we introduce
the concept of subcodes within a code and examine the relationship between
these subcodes and the ideals of a BCI-algebra over code C. Furthermore,
we define a binary relation among codewords and prove that code C, under
this relation—referred to as the (BCI)C -order—forms a partially ordered set.
Lastly, we show that the generator matrix of a binary linear code C contains
the minimal codewords of C with respect to the (BCI)C -order.
Keywords: BCI-algebra, binary linear block codes, subcodes, partially ordered set, lexicographic order
Published in RUNG: 05.12.2024; Views: 671; Downloads: 3
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9. Łukasiewicz anti fuzzy subalgebras of BCK/BCI-algebrasJeong Gi Kang, Hashem Bordbar, 2025, original scientific article Abstract: The subalgebra of BCK/BCI-algebra using Łukasiewicz anti fuzzy set
introduced by Jun is studied in this article. The concept of Łukasiewicz anti
fuzzy subalgebra of a BCK/BCI-algebra is introduced, and several properties are
investigated. The relationship between anti fuzzy subalgebra and Łukasiewicz anti
fuzzy subalgebra is given, and characterization of a Łukasiewicz anti fuzzy subalgebra
is discussed. Conditions are found in which a Lukasiewicz anti fuzzy set is a
Lukasiewicz anti fuzzy subalgebra Finally, conditions under which ⋖-subset, Υsubset, and anti-subset become subalgebra are explored.
Keywords: anti fuzzy subalgebra, Łukasiewicz anti fuzzy set, Łukasiewicz anti fuzzy, subalgebra, Υ-subset, anti subset
Published in RUNG: 30.10.2024; Views: 740; Downloads: 1
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10. A characterization of normal injective and normal projective hypermodulesErgül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, original scientific article Abstract: This study is motivated by the recently published papers on normal injective and normal
projective hypermodules. We provide a new characterization of the normal injective and normal
projective hypermodules by using the splitting of the short exact sequences of hypermodules. After presenting some of their fundamental properties, we show that if a hypermodule is normal projective, then every exact sequence ending with it is splitting. Moreover, if a hypermodule is a normal injective, then every exact sequence starting with it is splitting as well. Finally, we investigate the relationships between semisimple, simple, normal injective, and normal projective hypermodules.
Keywords: short exact sequence, normal injective hypermodule, normal projective hypermodule
Published in RUNG: 20.06.2024; Views: 1220; Downloads: 6
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