Group Codes Define Over Dihedral Groups of Small Order
Denis Chee-Keong Wong, Miin Huey Ang · 2013
The study of group codes as an ideal in a group algebra has been developed long time ago. If char(F) does not divides G , then FG is semisimple, and hence decomposes into a direct sum i i FG FGe = ⊕ where i FGe are minimal ideals generated by the idempotent ei. The idempotent ei provides some useful information on determining the minimum distance of group codes. In this paper, we study dihedral group codes generated by linear idempotents and nonlinear idempotents for dihedral groups of order 6, 8, 10 and 12. Our primary task is to determine the parameters of these families of group codes in order to obtain codes which near to attain the Singleton bound.