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On Lattice Packings and Coverings of Asymmetric Limited-Magnitude Balls

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arxiv 2005.14519 v1 pith:2N5R6HUB submitted 2020-05-29 cs.IT math.COmath.IT

Hengjia Wei , Xin Wang , Moshe Schwartz This is my paper · ORCID
classification cs.ITmath.COmath.IT
keywords codeserrorcoveringlimited-magnitudesetsappropriatearithmeticasymmetric
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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.

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