On tilings of asymmetric limited-magnitude balls
نویسندگان
چکیده
We study whether an asymmetric limited-magnitude ball may tile Z n . This generalizes previously studied shapes: crosses, semi-crosses, and quasi-crosses. Such tilings act as perfect error-correcting codes in a channel which changes transmitted integer vector bounded number of entries by errors. A construction lattice based on the Hamming metric is given. Several non-existence results are proved, both for general tilings, tilings. complete classification two certain cases proved.
منابع مشابه
On the Existence of Perfect Codes for Asymmetric Limited-Magnitude Errors
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2022
ISSN: ['1095-9971', '0195-6698']
DOI: https://doi.org/10.1016/j.ejc.2021.103450