Binary doubly-even self-dual codes of length 72 with large automorphism groups

We study binary linear codes constructed from fifty-four Hadamard 2-(71, 35, 17) designs. The constructed codes are self-dual, doubly-even and self-complementary. Since most of these codes have large automorphism groups, they are suitable for permutation decoding. Therefore we study PD-sets of the obtained codes. We also discuss the error-correcting capability of the obtained codes by majority logic decoding. Further, we describe a construction of a 3-(72, 12, 11) design and a 3-(72, 16, 2010) design from a binary [72, 16, 12] code, and a construction of a strongly regular graph with parameters (126, 25, 8, 4) from a binary [35, 8, 4] code related to a derived 2-(35, 17, 16) design.