Abstract
A two-dimensional code is defined as a set X ⊆ Σ** such that any picture over Σ is tilable in at most one way with pictures in X. The codicity problem is undecidable. The subclass of prefix codes is introduced and it is proved that it is decidable whether a finite set of pictures is a prefix code. Further a polynomial time decoding algorithm for finite prefix codes is given. Maximality and completeness of finite prefix codes are studied: differently from the one-dimensional case, they are not equivalent notions. Completeness of finite prefix codes is characterized.
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