| Title: | Ordered algebraic structure in a linear code |
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| Authors: | ID Bordbar, Hashem (Author) |
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| Files: |  http://dx.doi.org/10.3934/amc.2024052
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| Language: | English |
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| Work type: | Unknown |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | UNG - University of Nova Gorica
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| 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. |
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| Keywords: | BCI-algebra, binary linear block codes, subcodes, partially ordered set, lexicographic order |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | str. 1-12 |
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| Numbering: | Vol. , issue |
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| PID: | 20.500.12556/RUNG-9520  |
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| COBISS.SI-ID: | 217895683 |
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| UDC: | 51 |
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| ISSN on article: | 1930-5346 |
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| DOI: | 10.3934/amc.2024052 |
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| NUK URN: | URN:SI:UNG:REP:TFRDOB8B |
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| Publication date in RUNG: | 05.12.2024 |
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| Views: | 264 |
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| Downloads: | 2 |
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| Metadata: |    |
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