1. Computational algebra, coding theory and cryptography : theory and applicationsznanstvena 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: 210; Prenosov: 1
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4. The Structure of the Block Code Generated by a BL-AlgebraHashem 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: 2519; Prenosov: 59
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5. Codes generated by ordered algebraic structuresHashem bordbar, 2021, objavljeni povzetek znanstvenega prispevka na konferenci Opis: Error-control codes are used to detect and correct errors that occur when data are trans-mitted across some noisy channel or stored on some medium. The study of error-control codes is called coding theory and emerged in 1948 by Claud Shannon's paper which demonstrated that by proper encoding of the data, errors induced by a noisy channel can be reduced to any desired level without sacrificing the rate of information transmission. Some algebraic structures, includes the study and discovery of various coding schemes, are used to increase the number of errors that can be corrected during data transmission. One of the classes of logical algebra is ordered algebras which were introduced by Imai and Iseki in 1966. In this note, I study the codes generating by the ordered algebraic structures such as BCK-algebras and BL-algebras. For this goal, symmetric rela-tions on these ordered structures facilitate us to design the correspondence codeword. Moreover, I show that the structure of ordered algebra and the code generated by it will be the same. Ključne besede: coding theory, BCK-algebra, BL-algebra Objavljeno v RUNG: 20.08.2021; Ogledov: 3126; Prenosov: 152
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