Structure of linear codes invariant under the unitary group U(۳,۳)

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(۳,۳) and identify the complete set of linear codes derived from its ۲-representations.In addition, we use the supports of the codewords to construct certain designs that remain invariant under the action of U(۳,۳) and establish connections between these designs and the corresponding linear codes.

کلیدواژه ها:

Linear Codes ، Schur multiplier ، Support designs ، Unitary groups