A generalization of Niederreiter-Xing's propagation rule and its commutativity with duality

Niederreiter and Xing recently proposed A propagation rule for linear codes. Ozbudak and Stichtenoth [2] showed that the Niederreiter-Xing construction is a particular construction of a matrix-product code. In [4], Cheng, Cheng, and Sun analyzed the case when Niederreiter-Xing rule commutes with duality. The aim of this correspondence is to generalize the propagation rule to a wider class of codes and analyze the case when it commutes with duality.