S_h-sets and linear codes over \mathbbF_q

2024/11/28 by Viviana Carolina Guerrero Pantoja, Pantoja, Viviana Carolina Guerrero, John H. Castillo +3
Computer Science · Engineering · #11B13 #94B05 #94B65 #Advanced Wireless Network Optimization #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2411.19413

openalex publication_date 2024/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (G,+) be an Abelian group. Given h∈ ℤ⁺, a non-empty subset A of G is called an S_h-set if all the sums of h distinct elements of A are different. We extend the concept of S_h-set to a more general context in the context of finite vectorial spaces over finite fields. More precisely, a ∅ ≠ A⊆ \mathbbF_q^r is called an S_h-linear set if all the linear combinations of h elements of A are different. We establish a correspondence between q-ary linear codes and S_h-linear sets. This connection allow us to find lower bounds for the maximum size of S_h-sets in \mathbbF_q^r.

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