On the basis of the characteristics of cyclic codes, the codeword space can be partitioned into small subspaces where cyclically shifted codewords of a particular codeword occupy the same subspace. A cyclically permutable code generates codewords belonging to each subspace. However, no approach for the efficient construction of cyclically permutable code from binary cyclic codes has been proposed thus far. In this study, we propose an approach for the efficient and systematic construction of a cyclically permutable code from a cyclic code by utilizing an algebraic property. The proposed coding method improves the robustness of watermarking, particularly for video frames, against a clipping attack