1, We utilize computers to search the best generator matrix which let the proposed scheme have the best BER.

2, According to the generator matrix of a linear code, automorphism group is studied.

3, Due to the particular relation of generator matrix and parity check matrix, it can achieve unequal error protection performance with the modified decoding algorithm.

4, In chapter 3, we propose the methods for finding the generator matrix of a quasi-cyclic LDPC in"systematic form"from its parity-check matrix and its corresponding encoding schemes.

5, For the importance of the relationship between information and parity, the generator matrix and the parity-check matrix of every code have been discussed.

6, A new method for the construction of the high performance systematic irregular low-density parity-check (LDPC) codes based on the sparse generator matrix (G-LDPC) is introduced.

7, A novel Block Gauss Elimination(BGE) approach to construction of the generator matrix of quasi-cyclic low density parity check(QC-LDPC) codes is proposed.

8, Linear fuzzy error correcting code is discussed and such basic properties of linear fuzzy error correcting code as generator matrix,[http:///generator matrix.html] dual code and so on are studied.

9, These quasi-cyclic LDPC can not only reduce the storage of LDPC generator matrix, but also decrease the encoding complexity efficiently, which is of great significance for the applications.

10, In order to design codes with full-rate, quasi-orthogonal STBC (QO-STBC) was proposed, whose generator matrix was orthogonal between subspaces.

11, For information interception and signal analyzing of satellite communication system, it is usable if knows the generator matrix and information restoration matrix of Punctured convolutional codes.