On a class of linear codes whose automorphism group is dihedral

In this note, we define a class of linear codes whose automorphism group is the dihedral group of order eight (see theorem 9). To this aim, we first determine the weight distribution of these codes. Then we reduce the problem of automorphism of codes to the problem of automorphism of binary matrices and graphs. In particular, we establish a method to associate each code with a specific binary matrix, such that their automorphism group are isomorphic. We also use some theoritical software tools such as GAP, Magma and Q-extension.