Hadamard matrices of order 36 and double-even self-dual [72,36,12] codes

Abstract

Before this work, at least 762 inequivalent Hadamard matrices of order 36 were known. We found 7238 Hadamard matrices of order 36 and 522 inequivalent [72,36,12] double-even self-dual codes which are obtained from all 2-(35,17,8) designs with an automorphism of order 3 and 2 fixed points and blocks.

Keywords

• hadamard designs
• double-even self-dual codes
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-hc] computer science [cs]/human-computer interaction [cs.hc]