On Lattice Packings and Coverings of Asymmetric Limited-Magnitude Balls
Hengjia Wei, Xin Wang, Moshe Schwartz · IEEE Transactions on Information Theory · 2021
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 Bt-sequences, 2-fold Sidon sets, and sets avoiding arithmetic progression.