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PERFECT CODES IN THE HOMOGENEOUS METRIC
Published online by Cambridge University Press: 30 October 2025
Abstract
We study perfect codes in the homogeneous metric over the ring 
$\mathbb {Z}_{{2}^k}, k\ge 2$. We derive arithmetic nonexistence results from Diophantine equations on the parameters resulting from the sphere packing conditions, and a Lloyd theorem based on the theory of weakly metric association schemes.
MSC classification
Primary:
94B25: Combinatorial codes
Information
- Type
- Research Article
- Information
- Copyright
- © The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc
Footnotes
This research is supported by National Natural Science Foundation of China (Grant no. 12471490).
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