@article{1cbacf0c31ba499aa826a73962f1e5e5,
title = "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.",
keywords = "Integer coding, covering, lattices, limited-magnitude errors, packing, tiling",
author = "Hengjia Wei and Xin Wang and Moshe Schwartz",
note = "Funding Information: Manuscript received May 29, 2020; revised November 30, 2020; accepted March 12, 2021. Date of publication April 2, 2021; date of current version July 14, 2021. The work of Hengjia Wei and Moshe Schwartz was supported in part by the Israel Science Foundation (ISF) under Grant 270/18. The work of Xin Wang was supported in part by the National Natural Science Foundation of China under Grant 11801392 and in part by the Natural Science Foundation of Jiangsu Province under Grant BK20180833. (Corresponding author: Hengjia Wei.) Hengjia Wei and Moshe Schwartz are with the School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva 8410501, Israel (e-mail: hjwei05@gmail.com; schwartz@ee.bgu.ac.il). Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",
year = "2021",
month = aug,
day = "1",
doi = "10.1109/TIT.2021.3070462",
language = "English",
volume = "67",
pages = "5104--5115",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers",
number = "8",
}