Self-dual codes and Hadamard matrices

Abstract

A general method unifying known constructions of binary self-orthogonal codes from combinatorial designs and Hadamard matrices is described. As an application more than 80 inequivalent extremal doubly-even self-dual codes of length 40, 56 and 64 are constructed from Hadamard matrices of order 20 and 28 and symmetric 2-(31,10,3) designs. Many of these codes do not admit nontrivial automorphisms of odd orders, and there are codes with trivial automorphism groups.