| Naslov: | Ordered algebraic structure in a linear code |
|---|
| Avtorji: | ID Bordbar, Hashem (Avtor) |
|---|
| Datoteke: |  http://dx.doi.org/10.3934/amc.2024052
|
|---|
| Jezik: | Angleški jezik |
|---|
| Vrsta gradiva: | Neznano |
|---|
| Tipologija: | 1.01 - Izvirni znanstveni članek |
|---|
| Organizacija: | UNG - Univerza v Novi Gorici
|
|---|
| 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 |
|---|
| Status publikacije: | Objavljeno |
|---|
| Verzija publikacije: | Objavljena publikacija |
|---|
| Datum objave: | 01.01.2024 |
|---|
| Leto izida: | 2024 |
|---|
| Št. strani: | str. 1-12 |
|---|
| Številčenje: | Vol. , issue |
|---|
| PID: | 20.500.12556/RUNG-9520  |
|---|
| COBISS.SI-ID: | 217895683 |
|---|
| UDK: | 51 |
|---|
| ISSN pri članku: | 1930-5346 |
|---|
| DOI: | 10.3934/amc.2024052 |
|---|
| NUK URN: | URN:SI:UNG:REP:TFRDOB8B |
|---|
| Datum objave v RUNG: | 05.12.2024 |
|---|
| Število ogledov: | 263 |
|---|
| Število prenosov: | 2 |
|---|
| Metapodatki: |    |
|---|
|
:
|
Kopiraj citat |
|---|
| | | | Skupna ocena: | (0 glasov) |
|---|
| Vaša ocena: | Ocenjevanje je dovoljeno samo prijavljenim uporabnikom. |
|---|
| Objavi na: |  |
|---|
Postavite miškin kazalec na naslov za izpis povzetka. Klik na naslov izpiše
podrobnosti ali sproži prenos. |
