Summary: In this work we present a canonical-systematic form of a generator matrix for linear codes with respect to a hierarchical poset metric on the linear space \(\mathbb F_q^n\). We show that up to a linear isometry any such code is equivalent to the direct sum of codes with smaller dimensions. The canonical-systematic form enables to exhibit simple expressions for the generalized minimal weights (in the sense defined by Wei), the packing radius of the code, characterization of perfect codes and also a syndrome decoding algorithm that has (in general) exponential gain when compared to usual syndrome decoding.