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arXiv · 1706.03589

50 Years of the Golomb--Welch Conjecture

Peter Horak·Dongryul Kim
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Abstract

Since 1968, when the Golomb--Welch conjecture was raised, it has become the main motive power behind the progress in the area of the perfect Lee codes. Although there is a vast literature on the topic and it is widely believed to be true, this conjecture is far from being solved. In this paper, we provide a survey of papers on the Golomb--Welch conjecture. Further, new results on Golomb--Welch conjecture dealing with perfect Lee codes of large radii are presented. Algebraic ways of tackling the conjecture in the future are discussed as well. Finally, a brief survey of research inspired by the conjecture is given.

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Peter Horak, Dongryul Kim. 2017-06-12. 50 Years of the Golomb--Welch Conjecture. https://doi.org/10.1109/tit.2017.2786675

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