Hadamard-type block designs and self-dual codes
Any Hadamard design with parameters \((8m+3,4m+2,2m+1)\) can be used to obtain a self-dual doubly even \((16m+8,8m+4)-\)code [see \textit{V. K. Bhargava} and \textit{J. M. Stein}, Inf. Control 28, 352-355 (1975; Zbl 0311.94005)]. Trivially, for \(m=0\) the code has minimum weight \(d=4\). The author proves that \(d\geq 8\) for \(m\geq 1\), with equality for \(m=1\) and 2. For \(m=2\), one obtains exactly 3 nonequivalent (40,20)-codes in this way. The author also considers the cases \(m=3\) and 4.
scientific article; zbMATH DE number 3875145