Further results on the classification of binary self - dual [ 52 , 26 , 10 ] codes with an automorphism of odd prime order 1

The paper presents the next step on the complete classification of all optimal binary selfdual codes of length 52 that possess an automorphism of odd prime order. Applying the method for constructing binary self-dual codes with an automorphism of odd prime order p=3 we give full classification of all [52, 26, 10] binary self-dual codes with an automorphism of type 3-(16,4) for the next unsolved case for the generator matrix of the fixed subcode. Thus we construct 6494315 optimal codes with weight enumerator 52,2 ( ) W y for 1,4, β = and 7. Only a small portion of the codes we have obtained were previously known. Tables for the weight enumerators and order of the automorphism groups of all constructed codes are given.