ON THE AUTOMORPHISM GROUP OF SOME CLASSES OF SYSTEMATIC CODES

In several applications of algebraic coding theory and cryptography, we need only to compute an automorphism group of a linear code and not its full automorphism group which is known to be a hard problem. In this paper we give a more effective method for computing such a group of automorphisms of a systematic code C. In the particular case where [I|A] is a generator matrix of C and A is an involutory matrix the method described here can give important information about the full automorphism group and, in some cases, can even determine the full automorphism group. Numerical examples are given by use of some theoretical software tools such as GAP, Q-extension and Matlab.