فهرست نشریات علمی دسترسی آزاد ایران

In this paper, we outline a method for constructing linear codes invariant under primitive permutation groups. We will demonstrate that when a group $G$ possesses a trivial Schur multiplier, every binary linear code that admits $G$ as a permutation group can be regarded as a submodule of the permutation module within the primitive action of $G$. As an illustrative example, we select the finite simple group $G = U(3,3)$ and identify the complete set of linear codes derived from its 2-representations.In addition, we use the supports of the codewords to construct certain designs that remain invariant under the action of $U(3,3)$ and establish connections between these designs and the corresponding linear codes.