Abstract
We study whether an asymmetric limited-magnitude ball may tile Zn. 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.
Original language | American English |
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Title of host publication | IEEE Information Theory Workshop, ITW 2020 |
Pages | 1-5 |
Number of pages | 5 |
ISBN (Electronic) | 9781728159621 |
DOIs | |
State | Published - 22 Jun 2021 |
Event | 2020 IEEE Information Theory Workshop, ITW 2020 - Virtual, Riva del Garda, Italy Duration: 11 Apr 2021 → 15 Apr 2021 |
Conference
Conference | 2020 IEEE Information Theory Workshop, ITW 2020 |
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Country/Territory | Italy |
City | Virtual, Riva del Garda |
Period | 11/04/21 → 15/04/21 |
All Science Journal Classification (ASJC) codes
- Computational Theory and Mathematics
- Information Systems
- Signal Processing
- Software
- Theoretical Computer Science