Structure and measure of a decidable class of two-dimensional codes

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. It is in general undecidable whether a set X of pictures is a code also in the finite case. Very recently in [3] strong prefix picture codes were defined as a decidable subclass that generalizes prefix string codes. Here a characterization for strong prefix codes that results in an effective procedure to construct them is presented. As a consequence there are also proved interesting results on the measure of strong prefix codes and a connection with the family of string prefix codes.