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

Niederreiter and Xing (2000) recently proposed a propagation rule for linear codes.O/spl uml/zbudak and Stichtenoth showed that the Niederreiter-Xing construction is a particular construction of a matrix-product code. 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.