Hypergraph encoding set systems and their linear representations

2018/06/04 by Alberto Besana, Cristina Martínez, Besana, Alberto +2
Computer Science · Engineering · Mathematics · #05E10 #11T71 #Algebraic Geometry (math.AG) #Artificial intelligence #Coding theory and cryptography #Combinatorics #Combinatorics (math.CO) #Computer science #Cooperative Communication and Network Coding #Discrete mathematics #Encoding (memory) #FOS: Mathematics #Finite field #Finite set #Graph #Group (periodic table) #Hypergraph #Mathematics #Representation (politics) #Set (abstract data type) #Transitive relation #Vertex (graph theory) #graph theory and CDMA systems #math.AG #math.CO #msc:05E10 #msc:11T71

paper · pdf · doi:10.48550/arxiv.1806.01323

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2018/06/04 · arxiv created 2018/10/25 · arxiv updated 2018/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study t-designs of parameters (n,k,λ) over finite fields as group divisible designs and set systems admitting a transitive action of a linear group encoded in an hypergraph G whose vertex set of size n is partitioned into sets of size k in such a way that every t-subset is contained in at least λ subsets of G. We relate the problem to the representation theory of the general linear group \GL(n,\mathbbF_q) and the constructions of AG codes over finite fields.

Citations

• New directions in cryptography

Related

• S_h-sets and linear codes over \mathbbF_q
• AGC, t-designs and partition sets
• Tops of graphs of non-degenerate linear codes
• Large Sets of t-Designs over Finite Fields
• Codes and Orbit Covers of Finite Abelian Groups