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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| Sprache: | eng |
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| Zusammenfassung: | 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. |
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| DOI: | 10.48550/arxiv.2205.10574 |