Completely regular codes with covering radius 1 and the second eigenvalue in 3-dimensional Hamming graphs
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).
- Publication:
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arXiv e-prints
- Pub Date:
- March 2024
- DOI:
- 10.48550/arXiv.2403.02702
- arXiv:
- arXiv:2403.02702
- Bibcode:
- 2024arXiv240302702M
- Keywords:
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- Mathematics - Combinatorics