New extremal binary self-dual codes of length 64 from -lifts of the extended binary Hamming code
S Karadeniz, B Yildiz - Designs, Codes and Cryptography, 2015 - Springer
Designs, Codes and Cryptography, 2015•Springer
In this paper, we use the graded ring construction to lift the extended binary Hamming code
of length 8 to R_k R k. Using this method we construct self-dual codes over R_3 R 3 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 β= 1, 5, 13, 17, 21, 25, 29, 33, 41 and 52 in W …
of length 8 to R_k R k. Using this method we construct self-dual codes over R_3 R 3 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 β= 1, 5, 13, 17, 21, 25, 29, 33, 41 and 52 in W …
Abstract
In this paper, we use the graded ring construction to lift the extended binary Hamming code of length 8 to . Using this method we construct self-dual codes over 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 and 52 in and they all have automorphism groups of size 8.
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