Perfect codes in m-Cayley hypergraphs

Let G be a finite group with the identity e and S be a subset of G \ { e } such that S = S - 1 . Let m be an integer such that 2 <= m <= max { o ( s ) | s E S } , where o ( s ) is the order of s in G . The m-Cayley hypergraph H of G over S , m- Cay( G , S ), is a hypergraph with vertex set G and an edge set {{ s i x | 0 <= i <= m - 1 } | x E G , s E S } . We discover a necessary and sufficient condition for a subset S of G \ { e } such that a subgroup H is a perfect code in m- Cay( G , S ) and obtain some conditions for a subgroup H that guarantee the existence of a subset S subset of G \ { e } such that H is a perfect code in m-Cay( G , S ). (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.