condition on one - dimensional attracting sets of the simplest skew product of interval maps

In the theory of codes based on the Hamming metric, three classes of codes are well known, viz. cyclic codes, shortened cyclic codes and pseudocyclic codes. The important result is that a class of linear shortened cyclic codes coincides with a class of linear pseudocyclic codes [1]. There are no similar results in the theory of rank-metric based codes. In this paper, we generalize the notion of q-cyclic codes and introduce two new families of codes, viz. shortened q-cyclic codes and pseudo-q-cyclic codes. It is proved that a class of pseudo-q-cyclic codes coincides with a class of shortened q-cyclic codes if the number of positions to shorten is a multiple of the extension degree. The problem is still open to other shortening.