New extremal binary self-dual codes of lengths 64 and 66 from R2-lifts

Recently, Karadeniz and Yildiz introduced an efficient method to search for self-dual codes. It is called lifting method and can be applied to some alphabets. In this work, by considering R2-lifts of binary self-dual codes of length 16 new extremal binary self-dual codes of lengths 64 are constructed as Gray images. More precisely, we construct 15 new codes of length 64. Moreover, 10 new codes of length 66 were obtained by applying a building-up construction to the binary codes. Codes with these weight enumerators are constructed for the first time in the literature. The results are tabulated.