Classificação dos códigos perfeitos bidimensionais na métrica de Lee

In this paper, we present a description and the complete classification of all (linear and non linear) two-dimensional Lee-perfect Codes. Our results prove that in dimension two the codes constructed by Golomb-Welch [4] are essentially the only ones. We also present a complete description of all possible structures of Lee-perfect two-dimensional codes. An explicit “basis” for such codes is provided. Some results and techniques can be generalized to higher dimensions and could be helpful to approach the Golomb-Welch Conjecture in other cases.