论文标题
在晶格包装和不对称有限型球的覆盖物上
On Lattice Packings and Coverings of Asymmetric Limited-Magnitude Balls
论文作者
论文摘要
我们构建整数误差校正代码，并覆盖有限型误差通道的代码，并具有多个错误。代码是用适当的错误球打包或覆盖空间的晶格。其中一些结构达到了恒定的渐近包装/覆盖密度。结果是通过各种方法获得的，包括在锤式度量中使用代码，模块化$ b_t $ - 序列，$ 2 $ fold sidon sets，以及避免算术进展的集合。
We construct integer error-correcting codes and covering codes for the limited-magnitude error channel with more than one error. The codes are lattices that pack or cover the space with the appropriate error ball. Some of the constructions attain an asymptotic packing/covering density that is constant. The results are obtained via various methods, including the use of codes in the Hamming metric, modular $B_t$-sequences, $2$-fold Sidon sets, and sets avoiding arithmetic progression.
