Residue Code And Cyclic Code Over F_p+uF_p+u~2F_p

With the development and application of communication systems,algebraic coding technology,which is based on finite fields and represented by cyclic codes, has a rapid development. Over the last decade,the theory of error-correcting codes over finite rings has been hot researched. , it's becaused that under the Gray map several famous families of good nonlinear binary codes can be identified as images of linear codes over Z 4.Quadratic residue code is good cyclic code with high error-correcting capacity and its code rate is greater than or equal to1 2 .In this thesis, we study residue codes over finite fields and repeated-root codes over ring Fp + uFp + u 2Fp.As following:Biquadratic residue codes over F2 and the generator polynomials of cyclic codes of length p s over Fp + uFp + u 2Fp are researched.