Document Type
Article
Publication Date
11-2024
Abstract
Binary codes are constructed from incidence matrices of hypergraphs. A combinatorial 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. In particular the “eonv” method is used to prove that the minimum distance of codes from incidence matrices of complete 3-partite 3-uniform hypergraphs with partite set size of n is n2. A lower bound on the minimum distances of codes from a special class of circulant hypergraphs is also obtained. Moreover, self-duality and self-orthogonality conditions are also studied through hypergraphs.
Recommended Citation
Mallik, S., & Yildiz, B. (2022). Codes from incidence matrices of hypergraphs. The Art of Discrete and Applied Mathematics 7 (2024) #P3.10. https://doi.org/10.26493/2590-9770.1618.4eb
Comments
The copy of record is available from the publisher at https://adam-journal.eu/index.php/ADAM/article/view/1618/1575. This work is licensed under a Creative Commons CC-BY 4.0 license.