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arXiv · 2205.10574

A graphical representation of binary linear codes

Lisbeth Danyeli Delgado Ordoñez·John H. Castillo·Alexander Holguín-Villa
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Abstract

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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Lisbeth Danyeli Delgado Ordoñez, John H. Castillo, Alexander Holguín-Villa. 2022-05-21. A graphical representation of binary linear codes. https://arxiv.org/abs/2205.10574

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