2026/07/24 by John H. Castillo, Lisbeth D. Delgado-Ordoñez, Alexander Holguín-Villa
#cs.IT #math.IT
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, Γ(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.