On tilings of asymmetric limited-magnitude balls

Hengjia Wei, Moshe Schwartz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-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
Title of host publicationIEEE Information Theory Workshop, ITW 2020
PublisherInstitute of Electrical and Electronics Engineers
Pages1-5
Number of pages5
ISBN (Electronic)9781728159621
DOIs
StatePublished - 22 Jun 2021
Event2020 IEEE Information Theory Workshop, ITW 2020 - Virtual, Riva del Garda, Italy
Duration: 11 Apr 202115 Apr 2021

Conference

Conference2020 IEEE Information Theory Workshop, ITW 2020
Country/TerritoryItaly
CityVirtual, Riva del Garda
Period11/04/2115/04/21

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Information Systems
  • Signal Processing
  • Software
  • Theoretical Computer Science

Fingerprint

Dive into the research topics of 'On tilings of asymmetric limited-magnitude balls'. Together they form a unique fingerprint.

Cite this