Malaysian Journal of Mathematical Sciences, June 2015, Vol. 9(S)
Special Issue: The 4th International Cryptology and Information Security Conference 2014 (Cryptology 2014)

Group Ring Codes over a Dihedral Group

Zi Shyuan Tan, Miin Huey Ang and Wen Chean The

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A group ring code is a code that can be constructed using group rings. Linear codes have been associated to group rings since 1967. Many existing codes such as cyclic codes and abelian codes are specific examples of group ring codes. This study aims to answer whether there exists a group ring code that can never be a group ring code over a cyclic group. It is conceivable that it has a positive answer. However, our results on group ring codes over the dihedral group $D_6$ and $D_8$ do not support our belief. We found that every binary group ring code over $D_6$ ($D_8$ respectively) is equivalent to some binary group ring code over the cyclic group $C_6$($C_8$ respectively).

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