Group codes over binary tetrahedral group

Abstract In this article, the group algebra K [ T ] {\mathcal{K}}\left[{\mathscr{T}}] of the binary tetrahedral group T {\mathscr{T}} over a splitting field K {\mathcal{K}} of T {\mathscr{T}} with char ( K ) ≠ 2 , 3 {\rm{char}}\left({\mathcal{K}})\ne 2,3 is studied and the unique idempotents corresponding to all seven characters of the binary tetrahedral group are computed. Furthermore, the minimum weights and dimensions of various group codes generated by linear and nonlinear idempotents in this group algebra are characterized to establish these group codes.