New extremal binary self-dual codes of length 64 from R₃-lifts of the extended binary Hamming code

In this paper, we use the graded ring construction to lift the extended binary Hamming code of length 8 to R_k. Using this method we construct self-dual codes over R₃ of length 8 whose Gray images are self-dual binary codes of length 64. In this way, we obtain twenty six non-equivalent extremal binary Type I self-dual codes of length 64, ten of which have weight enumerators that were not previously known to exist. The new codes that we found have β = 1, 5, 13, 17, 21, 25, 29, 33, 41 and 52 in W_64,2 and they all have automorphism groups of size 8.