1. On tilings of asymmetric limited-magnitude balls.
- Author
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Wei, Hengjia and Schwartz, Moshe
- Subjects
- *
CHANNEL coding , *TILING (Mathematics) , *HAMMING codes , *ERROR-correcting codes - Abstract
We study whether an asymmetric limited-magnitude ball may tile Z n. This ball generalizes previously studied shapes: crosses, semi-crosses, and quasi-crosses. Such tilings act as perfect error-correcting codes in a channel which changes a transmitted integer vector in a bounded number of entries by limited-magnitude errors. A construction of lattice tilings based on perfect codes in the Hamming metric is given. Several non-existence results are proved, both for general tilings, and lattice tilings. A complete classification of lattice tilings for two certain cases is proved. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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