Codes from incidence matrices of hypergraphs

Sudipta Mallik; Bahattin Yildiz

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arXiv · 2210.06733

Codes from incidence matrices of hypergraphs

Sudipta Mallik·Bahattin Yildiz

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Abstract

Binary codes are constructed from incidence matrices of hypergraphs. A combinatroial description is given for the minimum distances of such codes via a combinatorial tool called ``eonv". This combinatorial approach provides a faster alternative method of finding the minimum distance, which is known to be a hard problem. This is demonstrated on several classes of codes from hypergraphs. Moreover, self-duality and self-orthogonality conditions are also studied through hypergraphs.

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Sudipta Mallik, Bahattin Yildiz. 2022-10-13. Codes from incidence matrices of hypergraphs. https://arxiv.org/abs/2210.06733

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