New Self-Dual and Formally Self-Dual Codes from Group Ring Constructions

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Advances in Mathematics of Communications following peer review. The definitive publisher-authenticated version Dougherty, S., Gildea, J., Kaya, A., & Yildiz, B. (2019). New Self-Dual and Formally Self-Dual Codes from Group Ring Constructions. Advances in Mathematics of Communications will be available when published online at http://www.aimsciences.org/journal/1930-5346In 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 $_F2 +uF_2$ and $F_4 + uF_4$, we obtain 9 new extremal binary self-dual codes of length 68 and 25 even formally self-dual codes with parameters [72,36,14]