2012/08/22 by Daniel R. Hawtin, Hawtin, Daniel R., Neil I. Gillespie +3
Computer Science · Engineering · Mathematics · #05E18 #94B60 #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.CO #math.IT #msc:05E18 #msc:94B60
paper · pdf · doi:10.48550/arxiv.1208.4455
openalex publication_date 2012/08/22 · arxiv created 2014/05/08 · arxiv updated 2014/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We construct a new infinite family of elusive pairs, where the group in question acts transitively on the set of neighbours of the code. In our examples, we find that the alphabet size always divides the length of the code, and prove that there is no elusive pair for the smallest set of parameters for which this is not the case. We also pose several questions regarding elusive pairs.