TY - JOUR
T1 - On Tilings of Asymmetric Limited-Magnitude Balls.
AU - Wei, Hengjia
AU - Schwartz, Moshe
N1 - Funding Information:
This work was supported in part by an Israel Science Foundation (ISF) grant 270/18 .
Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2022/2/1
Y1 - 2022/2/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85117695135&partnerID=8YFLogxK
U2 - 10.1016/j.ejc.2021.103450
DO - 10.1016/j.ejc.2021.103450
M3 - Article
SN - 0195-6698
VL - 100
SP - 1
EP - 21
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 103450
ER -