Hadamard-Type Block Designs and Self-Dual Codes

The article considers binary self-dual doubly even $(16m+8,8m+4)$ codes with generating matrix that is specified by means of the incidence matrix of a Hadamard block design with parameters $2-(8m+3,4m+2,2m+1)$. It is shown that for $m>0$ the minimum weight of the code is equal to at least 8. Codes for $m\leq 2$ are extremal. It is shown that the six nonisomorphic $2-(19,10,5)$ block designs yield three nonequivalent extremal $(40,20)$ codes.