The edge code of hypergraphs
Journal article, 2025
Given a hypergraph ℍ, we introduce a new class of evaluation toric codes called edge codes derived from ℍ. We analyze these codes, focusing on determining their basic parameters. We provide estimations for the minimum distance, particularly in scenarios involving d-uniform clutters. Additionally, we demonstrate that these codes exhibit self-orthogonality. Furthermore, we compute the minimum distances of edge codes for all graphs with five vertices.
hypergraphs
toric codes
squarefree evaluation codes
e torus
degree
Edge codes
footprint
Gröbner basis
next-to-minimal weights
finite field
Author
Delio Jaramillo Velez
Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks
Journal of Algebra and its Applications
0219-4988 (ISSN) 17936829 (eISSN)
2541003Subject Categories (SSIF 2025)
Computer Sciences
Discrete Mathematics
DOI
10.1142/S0219498825410038