Hypergraph encoding set systems and their linear representations

2018/06/04 by Alberto Besana, Cristina Martínez, Besana, Alberto +1
Computer Science · Engineering · #05E10 #11T71 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1806.01323

openalex publication_date 2018/06/04 · 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