The Automorphism Group Of Linear Code

The research about the automorphism group of linear code is basic in coding theory. It is very important for the design of decoding algorithm, the design and analyses of cryptogram system. But generally speaking, finding the automorphism group of linear code is very difficult. In bibliography [18] and [20], through using generalized inverse to find the automorphism group of linear code is a more effective method. But the computational quantity is very huge, so it is necessary to find a more effective way to induce the computational quantity. Based on the bibliography [12], [19] and [21], in this thesis, we do further research on the automorphism group of linear code, and obtain some of the following results.1. According to the automorphism group of linear code is equal to the dual codeover finite field F₂, using the property of the parity check matrix ,the computation of theautomorphism group of linear code is simplified.2. The automorphism group of linear equiweight code over anarbitrary finite field is given.3. Arbitrary linear code is equivalent to systematic code, and the equivalent code's automorphism is also isomorphism, so the computation is also simplified.