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arXiv · 2607.22800

Operations on binary linear codes and their associated graphs

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

This manuscript addresses a connection between operations in coding theory and graph theory, as well as some operations in both areas. The concept of the Hasse diagram of a binary linear code, $\Gamma(C)$, is recall; this concept visually represents the cosets of a binary linear code with a partial ordering. The main objetive is to give a characterization of the graphs corresponding to: extended codes, punctured codes, and the direct sum of two codes, using the graph of the given binary linear code as a starting point. Relationships are established between the graphs of code operations and particular operations of graphs.

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John H. Castillo, Lisbeth D. Delgado-Ordoñez, Alexander Holguín-Villa. 2026-07-24. Operations on binary linear codes and their associated graphs. https://arxiv.org/abs/2607.22800

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