Completely regular codes with covering radius 1 and the second eigenvalue in 3-dimensional Hamming graphs

2024/03/05 by Mogilnykh, Ivan, Taranenko, Anna, Vorob'ev, Konstantin
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.02702

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).

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