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.
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Delio Jaramillo-Velez (2024) studied this question.
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