50 Years of the Golomb--Welch Conjecture

摘要

Since 1968, when the Golomb--Welch conjecture was raised, it has become themain 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 tobe true, this conjecture is far from being solved. In this paper, we provide asurvey of papers on the Golomb--Welch conjecture. Further, new results onGolomb--Welch conjecture dealing with perfect Lee codes of large radii arepresented. Algebraic ways of tackling the conjecture in the future arediscussed as well. Finally, a brief survey of research inspired by theconjecture is given.