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.