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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: 151; Prenosov: 1
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Opis: This manuscript aims to provide a new characterization of Sheffer stroke Hilbert algebras due to their ideals and proposes stabilizers. In the setup of the main results, we construct particular subsets of Sheffer stroke Hilbert algebras and we propose important properties of these subsets by investigating whether these sets are ideals or not. Furthermore, we investigate whether the introduced subsets of Sheffer stroke Hilbert algebras are minimal ideals. Afterward, we define stabilizers in a Sheffer stroke Hilbert algebra and obtain their set theoretical properties. As an implementation of the theoretical findings, we present numerous examples and illustrative remarks to guide readers.
Ključne besede: Hilbert algebra, Sheffer operation, ideal, stabilizer
Objavljeno v RUNG: 31.01.2024; Ogledov: 1341; Prenosov: 8
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Opis: We describe and motivate our project for a hypercompositional approach to quantum logic.
Ključne besede: quantum logic, hypercompositional algebra, hypergroups, lattice, projective geometry
Objavljeno v RUNG: 01.08.2023; Ogledov: 1532; Prenosov: 4
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Ključne besede: Linear algebra, Networks/graphs, Linear programming
Objavljeno v RUNG: 15.02.2023; Ogledov: 1934; Prenosov: 1
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Ključne besede: symmetry, hypercompositional algebra, special issue
Objavljeno v RUNG: 17.10.2022; Ogledov: 1840; Prenosov: 23
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