Abstract:In order to promote the application in project of dual codes over the finite chain ring, the structure of dual codes (N=psn) over R=Fp[u]/<uk> was investigated. By MS polynomial of cyclic codes in finite chain ring of R, the theorem of the relationship between Hermitian inner product in R and the coefficients of discrete Fourier transforms was derived. It was proved that dual codes of C were annihilator code C under the conjugate map image to obtain the structures of dual codes over R=Fp[u]/<uk>. A theoretical basis is provided for the application of coding and decoding codes over finite chain ring. The foundation is established for the feasible of the light-weight code-based cryptosystems with anti-quantum computing properties in practical application.