Cross-bifix-free sets in two dimensions

A bidimensional bifix (in short bibifix) of a square matrix T is a square submatrix of T which occurs in the top-left and bottom-right corners of T. This allows us to extend the definition of bifix-free words and cross-bifix-free set of words to bidimensional structures. In this paper we exhaustively generate all the bibifix-free square matrices and we construct a particular non-expandable cross-bibifix-free set of square matrices. Moreover, we provide a Gray code for listing this set.