Edge codes constructed from unicyclic graphs

@misc{asensio2026edge,
  title = {{Edge codes constructed from unicyclic graphs}},
  author = {Sara Asensio and Giulia Gaggero and Naveena Ragunathan and Abhilash Saha and Adam Van Tuyl},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30407},
  eprint = {2608.30407},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30407},
}

TY  - UNPB
TI  - Edge codes constructed from unicyclic graphs
AU  - Sara Asensio
AU  - Giulia Gaggero
AU  - Naveena Ragunathan
AU  - Abhilash Saha
AU  - Adam Van Tuyl
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30407
UR  - https://arxiv.org/abs/2608.30407
AB  - Jaramillo-Velez recently introduced edge codes, a new class of toric evaluation codes constructed from the edges of a (hyper)graph ℋ. In the case that ℋ is a tree, Jaramillo-Velez computed both the minimum distance and the weight distribution of the associated code. In this paper, we study edge codes associated to unicyclic graphs. Our most striking result is that computing the parameters of these codes is subtle in the case that the induced cycle has an even length because these values will depend on certain conditions regarding the length of the cycle and the size of the base field.
ER  -