On the [24, 12, 10] quaternary code and binary codes with an automorphism having two cycles

A general decomposition theorem is given for codes over finite fields which have an automorphism of a given type. Such codes can be decomposed as direct sums of subcodes which may be viewed as shorter length codes over extension fields. If such a code is self-dual, sometimes the subcodes are also. This decomposition is applied to prove that the self-dual [24, 12, 10] quaternary code has no automorphism of order 3. This decomposition is also applied to count the number of equivalent [2r, r] and [2r+2r+1] self-dual binary codes with an automorphism of prime order r