A graphical representation of binary linear codes
A binary $[n,k]$-linear code $\mathcal{C}$ is a $k$-dimensional subspace of $\mathbb{F}_2^n$. For $\boldsymbol{x}\in \mathbb{F}_2^n$, the set $\boldsymbol{x}+\mathcal{C}$ is a coset of $\mathcal{C}$. In this work we study a partial ordering on the set of cosets of a binary linear code $\mathcal{C}$...
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| creator | Ordoñez, Lisbeth Danyeli Delgado Castillo, John H Holguín-Villa, Alexander |
| description | A binary $[n,k]$-linear code $\mathcal{C}$ is a $k$-dimensional subspace of
$\mathbb{F}_2^n$. For $\boldsymbol{x}\in \mathbb{F}_2^n$, the set
$\boldsymbol{x}+\mathcal{C}$ is a coset of $\mathcal{C}$. In this work we study
a partial ordering on the set of cosets of a binary linear code $\mathcal{C}$
of length $n$ and we construct a graph using the orphan structure of this code. |
| doi_str_mv | 10.48550/arxiv.2205.10574 |
| format | Article |
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$\boldsymbol{x}+\mathcal{C}$ is a coset of $\mathcal{C}$. In this work we study
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| subjects | Computer Science - Information Theory Mathematics - Information Theory |
| title | A graphical representation of binary linear codes |
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