Research On Some Problems Of Error-correcting Codes Constructed From Hadamard Matrices

Hadamard matrices are special matrices and different rows are orthogonal.Hadamard matrices includes normal Hadamard matrices , skew Hadamard matrices , skew-normal Hadamard matrices , complex Hadamard matrices , symmetric Hadamard matrices and more generalized matrices etc.Let H_n be a normalized Hadamard matrices, if +1's are replaced by 0's and -1's by 1's, H_n is changed into the binary Hadamard matrix A_n. Codes Constructed from A_n are Hadamard codes.In this text , new (0, 1) and (0, -1, 1) matrices constructed from normal Hadamard matrices , skew-normal Hadamard matrices and the Core of skew-normal Hadamard matrices. Codes are generated from them. The code's properties are researched, it is proved sufficient condition and necessary condition that the codes is self-orthogonal codes and self-dual codes.