New self-dual and formally self-dual codes from group ring constructions

Abstract

In this work, we study construction methods for self-dual and formally self-dual codes from group rings, arising from the cyclic group, the dihedral group, the dicyclic group and the semi-dihedral group. Using these constructions over the rings F2 + uF2 and F4 + uF4, we obtain 9 new extremal binary self-dual codes of length 68 and 25 even formally self-dual codes with parameters [72, 36, 14].