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

Abstract

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 error-correcting capability of the obtained codes
by majority logic decoding. Further, we describe 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.