New Constructions Of Orbit Codes And LDPC Codes

In communication systems,the coding technology is used to improve the transmission efficiency and the reliability of digital systems.In order to meet people's requirements for digital systems,it is particularly important to study new coding schemes.In this paper,we study new coding schemes of orbit codes and LDPC codes.Firstly,two operations of subspace codes are given.Based on the suborbits of permutation groups and the direct sum of groups,orbit codes with better parameters are constructed and an example of spread codes is given;A condition of orbit codes with constant distance is obtained.Based on the companion matrix of primitive polynomials over finite fields,a non-cyclic orbit code is constructed,a condition of the optimal non-cyclic orbit codes is obtained and an example of optimal codes is given.Secondly,based on the inclusion relation of subspaces in symplectic spaces,a binary LDPC code is constructed.Furthermore,we study that the girth of Tanner graph of LDPC codes is 6.Finally,a non-binary LDPC code is constructed based on the partition over finite fields.The simulation results show that our scheme is better than the scheme 2 constructed by Lin,when code length and code rate are same.