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On tilings of asymmetric limited-magnitude balls.
- Source :
-
European Journal of Combinatorics . Feb2022, Vol. 100, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
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]
- Subjects :
- *CHANNEL coding
*TILING (Mathematics)
*HAMMING codes
*ERROR-correcting codes
Subjects
Details
- Language :
- English
- ISSN :
- 01956698
- Volume :
- 100
- Database :
- Academic Search Index
- Journal :
- European Journal of Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 153622506
- Full Text :
- https://doi.org/10.1016/j.ejc.2021.103450