非对称有限球的格填充与覆盖
On Lattice Packings and Coverings of Asymmetric Limited-Magnitude Balls
摘要：
对于有限误差信道，我们构造了整数纠错码和覆盖码。代码是用适当的错误球填充或覆盖空间的网格。一些结构达到一个渐近的包装/覆盖密度是恒定的。结果是通过各种方法，包括使用代码的汉明度量，模块化$B_t$ -序列，$2$倍西顿集，避免算术级数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
