Completely regular codes with covering radius 1 and the second eigenvalue in 3-dimensional Hamming graphs
Combinatorics
2024-03-06 v1
Abstract
We obtain a classification of the completely regular codes with covering radius 1 and the second eigenvalue in the Hamming graphs H(3,q) up to q and intersection array. Due to works of Meyerowitz, Mogilnykh and Valyuzenich, our result completes the classifications of completely regular codes with covering radius 1 and the second eigenvalue in the Hamming graphs H(n,q) for any n and completely regular codes with covering radius 1 in H(3,q).
Keywords
Cite
@article{arxiv.2403.02702,
title = {Completely regular codes with covering radius 1 and the second eigenvalue in 3-dimensional Hamming graphs},
author = {Ivan Mogilnykh and Anna Taranenko and Konstantin Vorob'ev},
journal= {arXiv preprint arXiv:2403.02702},
year = {2024}
}