New results on the classification of binary self - dual [ 52 , 26 , 10 ] codes with an automorphism of odd prime order 1
نویسندگان
چکیده
The paper presents an important step toward the complete classification of all optimal binary self-dual codes of length 52 that possess an automorphism of odd prime order. Using a method for constructing and classifying binary self-dual codes with an automorphism of odd prime order p we give full classification of all [52, 26, 10] binary self-dual codes with an authomorphism of type 3-(16,4) and a certain generator matrix for the fixed subcode. Also, we construct 178727 optimal codes with weight enumerator 52,1 ( ) W y . All but one of the constructed codes are new. For all constructed codes we give the order of its automorphism group.
منابع مشابه
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...
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