A design and a code invariant under the simple group Co3

Mathematics;mathematics

A class of non-embeddable designs

AbstractA sufficient condition for non-embeddability of quasi-derived designs into symmetric designs is proved. Using this condition, several series of non-embeddable designs are constructed

Self-orthogonal designs and extremal doubly even codes

A general method unifying the known constructions of binary self-orthogonal codes from designs is described. As an application more than 70 inequivalent extremal doubly even self-dual codes of length 40 are constructed from Hadamard matrices of order 20. Some of these codes do not admit nontrivial automorphisms of odd orders, and there is a code with trivial automorphism group