The Research Of The Automorphism Group Of Linear Code

The research about the automorphism group of linear code is a foundation in coding theory. It is also a cornerstone for decoding and cryptography. Therefore, the research about the automorphism group of linear code is very important.Combining group theory, finite field, linear programming, the theory of generalized inversen matrix with the theory of coding, this dissertation obtains the following results.(1) We provide an constructive algorithm of the automorphism group of linear code.(2) In the projected space on Fq field, we present the automorphism group of linear equiweight code by a constructive way.(3) The theorems on the automorphism permutation of the quadratic-residue codes are established. The correct of theorems is checked by two exampes.