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1.
Computational algebra, coding theory and cryptography : theory and applications
znanstvena monografija

Opis: 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.
Ključne besede: algebraic structures, coding theory, cryptography, linear codes, quantum codes, polycyclic codes, self-dual codes, Hermitian codes, quasicyclic codes, codes over rings
Objavljeno v RUNG: 03.02.2025; Ogledov: 151; Prenosov: 0
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2.
Ordered algebraic structure in a linear code
Hashem Bordbar, 2024, izvirni znanstveni članek

Opis: 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.
Ključne besede: BCI-algebra, binary linear block codes, subcodes, partially ordered set, lexicographic order
Objavljeno v RUNG: 05.12.2024; Ogledov: 487; Prenosov: 2
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3.
Computational algebra, coding theory, and cryptography : theory and applications
Hashem Bordbar, 2024, drugi znanstveni članki

Ključne besede: ring theory, coding theory, cryptography, linear codes, field theory
Objavljeno v RUNG: 15.11.2024; Ogledov: 493; Prenosov: 3
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4.
The Structure of the Block Code Generated by a BL-Algebra
Hashem Bordbar, 2022, izvirni znanstveni članek

Opis: 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.
Ključne besede: BL-function, BL-code, binary linear block codes, coding theory, BL-algebra
Objavljeno v RUNG: 07.03.2022; Ogledov: 2492; Prenosov: 57
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5.
BCK codes
Hashem Bordbar, 2022, izvirni znanstveni članek

Opis: In this paper, we initiate the study of the notion of the BC K -function on an arbitrary set A, and providing connections with x -functions and x -subsets for x ∈ X where X is a B C K -algebra. Moreover, using the notion of order in a B C K -algebra, the BCK-code C is introduced and besides a new structure of order in C is investigated. Finally, we show that the structure of the B C K -algebra X and the B C K -code C which is generated by X , with their related orders are the same.
Ključne besede: BCK -function, x-functions, x-subsets, BCK -codes, binary linear block codes
Objavljeno v RUNG: 04.01.2022; Ogledov: 2375; Prenosov: 10
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