2022/11/06 by Junyang Zhang, Zhang, Junyang · 4 citations
Computer Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2211.03120
openalex publication_date 2022/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A perfect code in a graph Γ is a subset C of V(Γ) such that no two vertices in C are adjacent and every vertex in V(Γ)∖ C is adjacent to exactly one vertex in C. Let G be a finite group and C a subset of G. Then C is said to be a perfect code of G if there exists a Cayley graph of G admiting C as a perfect code. It is proved that a subgroup H of G is a perfect code of G if and only if a Sylow 2-subgroup of H is a perfect code of G. This result provides a way to simplify the study of subgroup perfect codes of general groups to the study of subgroup perfect codes of 2-groups. As an application, a criterion for determining subgroup perfect codes of projective special linear groups PSL(2,q) is given.