Naslov
S-Elusive Codes in Hamming Graphs

Autori
Hawtin, Daniel

Izvornik
Designs, codes and cryptography (0925-1022) 89 (2021), 6; 1211-1220

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
s-elusive codes ; Hamming graph

Sažetak
A code is a subset of the vertex set of a Hamming graph. The set of s-neighbours of a code is the set of all vertices at Hamming distance s from their nearest codeword. A code C is s-elusive if there exists a distinct code C′ that is equivalent to C under the full automorphism group of the Hamming graph such that C and C′ have the same set of s-neighbours. We show that the minimum distance of an s-elusive code is at most 2s + 2, and that an s- elusive code with minimum distance at least 2s + 1 gives rise to a q-ary t-design with certain parameters. This leads to the construction of: an infinite family of 1-elusive and completely transitive codes, an infinite family of 2-elusive codes, and a single example of a 3-elusive code. Answers to several open questions on elusive codes are also provided.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA