On Tilings of Asymmetric Limited-Magnitude Balls.

Hengjia Wei, Moshe Schwartz

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number103450
JournalEuropean Journal of Combinatorics
Volume100
DOIs
StatePublished - 1 Feb 2022

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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