Geodesic
Semisimple group codes and dihedral codes
Algebra and discrete mathematics, no. 3 (2009), pp. 28-48 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider codes that are given as two-sided ideals in a semisimple finite group algebra ${\mathbb F}_qG$ defined by idempotents constructed from subgroups of $G$ in a natural way and compute their dimensions and weights. We give a criterion to decide when these ideals are all the minimal two-sided ideals of ${\mathbb F}_qG$ in the case when $G$ is a dihedral group and extend these results also to a family of quaternion group codes. In the final section, we give a method of decoding; i.e., of finding and correcting eventual transmission errors.
Keywords: group algebra, idempotent, dihedral group
Mots-clés : group code, minimal code, quaternion group. 
@article{ADM_2009_3_a3,
     author = {Flaviana S. Dutra and Raul A. Ferraz and C. Polcino Milies},
     title = {Semisimple group codes and dihedral codes},
     journal = {Algebra and discrete mathematics},
     pages = {28--48},
     year = {2009},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2009_3_a3/}
}
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Flaviana S. Dutra; Raul A. Ferraz; C. Polcino Milies. Semisimple group codes and dihedral codes. Algebra and discrete mathematics, no. 3 (2009), pp. 28-48. http://geodesic.mathdoc.fr/item/ADM_2009_3_a3/