Affiliation:
1. Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill , Shimla-171005 , India
Abstract
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.
Subject
Applied Mathematics,Computational Mathematics,Computer Science Applications
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