Cocyclic codes of length 40 (Q5947249)

The author is looking for extremal self-dual codes, i.e. self-dual codes for which the minimal distance is maximal in the sense that it attains the value \(d= 4[n/24]+ 4\), which is the maximum value in case the code is doubly even. In order to find such codes, he looks at a particular construction method for self-dual codes involving Hadamard matrices. As a further restriction, he imposes the Hadamard matrices (and hence the codes) to be cocyclic with respect to certain groups. Using known constructions for cocylic Hadamard matrices, he is thus able to classify the self-dual codes found in this way and to group them into a limited number of equivalence classes. This allows him in the case of length 40 to calculate the minimal distance of all codes constructed in the above way, and to spot the extremal ones.