论文标题
在不对称有限速度球的瓷砖上
On Tilings of Asymmetric Limited-Magnitude Balls
论文作者
论文摘要
我们研究不对称的有限型球是否可以瓷砖$ \ mathbb {z}^n $。该球概括了先前研究的形状：十字架，半十字和准杂交。这种瓷砖在通道中充当完美的误差校正代码，该通道通过有限的数量误差在有限数量的条目中更改传输的整数向量。 给出了基于锤子指标中完美代码的晶格砖的结构。对于一般瓷砖和晶格砖，证明了几种不存在的结果。证明了两种特定情况的晶格瓷砖的完整分类。
We study whether an asymmetric limited-magnitude ball may tile $\mathbb{Z}^n$. 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.
