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Let P be a poset on the set [m]×[n], which is given as the disjoint sum of posets on ’columns’ of [m]×[n], and let P̌ be the dual poset of P. Then P is called a generalized Niederreiter-Rosenbloom-Tsfasman poset (gNRTp) if all further posets on columns are weak order posets of the ’same type’. Let G (resp. Ǧ) be the group of all linear automorphisms of the space ${}_q^{m\times n}$ preserving the P-weight (resp. P̌-weight). We define two partitions of ${}_q^{m\times n}$, one consisting of ’P-orbits’ and the other of ’P̌-orbits’....