On commutativity of duality operator and propagation operator of linear codes generated from algebraic curves

Based on the construction of linear codes proposed by Niederriter and Xing (see Applicable Algebra in Engineering, Communication and Computing, vol.10, p.425-32, 2000), a corresponding generator matrix is derived. The duality operator and the propagation operator of these extended linear codes are studied. A sufficient and necessary condition under which these two operators are commutative is obtained. This commutative property is found useful for constructing the corresponding parity-check matrix and, thus, the error detection/recovery codes.