2020/05/30 by Hengjia Wei, Wei, Hengjia, Moshe Schwartz +1 · 1 citation
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2006.00198
openalex publication_date 2020/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.