New extremal binary self-dual codes of length 64 from $$R_3$$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 $$R_k$$Rk. Using this method we construct self-dual codes over $$R_3$$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 $$\beta = 1, 5, 13, 17, 21, 25, 29, 33, 41$$β=1,5,13,17,21,25,29,33,41 and 52 in $$W_{64,2}$$W64,2 and they all have automorphism groups of size 8.

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