Malaysian Journal of Mathematical Sciences, August 2013, Vol. 7(S)
Special Issue: The 3rd International Conference on Cryptology & Computer Security 2012 (CRYPTOLOGY2012)
Group Codes Define Over Dihedral Groups of Small Order
Denis C. K. Wong and Ang M. H.
Corresponding Email: deniswong@utar.edu.my
Received date: -
Accepted date: -
Abstract:
The study of group codes as an ideal in a group algebra has been developed long time ago. If char(F) does not divides $\left | G \right |$, then $FG$ is semisimple, and hence decomposes into a direct sum $FG=\underset{i}{\oplus}FGe_{i}$ where $FGe_{i}$ are minimal ideals generated by the idempotent $e_i$. The idempotent $e_i$ 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.
Keywords: Group algebra, group codes, Singleton bound, linear idempotents, nonlinear idempotents
Indexing
