LDPC Codes And Constacvclic Codes Over Several Classes Of Finite Rings

Based on coding theory of finite fields,m-MDS linear codes over finite fields are generalized to almost m-MDS linear codes.And then based on the construction theory of LDPC codes and elementary techniques,the dual codes and some properties for several classes of LDPC codes over finite fields are determined.Furthermore,some new examples for m-MDS linear codes over finite fields are obtained,where m is a nonnegative integer.Basing on coding theory of finite rings and algebraic properties,the present thesis gives a sufficient and necessary condition for the existence of non-trivial self-orthogonal cyclic codes over the ring Zp1p2…pt and the corresponding explicit enumerating formula,and then proves that there doesn't exist any self-dual cyclic code over Zp1p2…pt,where pi(i?1,2,…,t)are distinct primes.