On Lattice Packings and Coverings of Asymmetric Limited-Magnitude Balls
Abstract
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.