The Sd_q On The Finite Chain Ring On The Cyclic Code Of Mattson's The-solomn Polynomials And Finite Fields (b) Code

In this paper, we study two kinds of error-correcting codes. One kind is cyclic code over finite chain rings, and the other is SDq(b) code over finite fields. As to cyclic codes over finite chain rings, we study their stucture and develop the Fourier Transform method to finite chain rings. The permutation groups of cyclic codes and their extended codes are investigated using their Mattson-Solomn polynomials. SDq(b) codes over finite fields are byte-organized and they can correct any single error and detect all double-ajacent errors in the same byte. For SDq(b) codes satisfying q>3,b>2 over finite field Fq, we give a lower bound than the pairs bound.