The edge code of hypergraphs
<|reference_start|>The edge code of hypergraphs: Given a hypergraph $\mathcal{H}$, we introduce a new class of evaluation toric codes called edge codes derived from $\mathcal{H}$. 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.<|reference_end|>
@article{jaramillo-velez2024the,
    title={The edge code of hypergraphs},
    author={Delio Jaramillo-Velez},
    journal={arXiv preprint arXiv:2404.02301},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.02301},
    primaryClass={math.AC cs.IT math.CO math.IT}
}