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Let G be a finite abelian group and F a field such that char(F) | |G|. Denote by FG the group algebra of G over F. A (semisimple) abelian code is an ideal of FG. Two codes I1 and I2 of FG are G-equivalent if there exists an automorphism ψ of G whose linear extension to FG maps I1 onto I2.In this paper we give a necessary and sufficient condition for minimal abelian codes to be G-equivalent and show how to correct some results in the literature.Index Terms-group algebra, G-equivalence, primitive idempotent, abelian codes.

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Let G be a finite group. Berman [Dokl. Akad. Nauk 106 (1956) 767] and Witt [J. Reine Angew. Math. 190 (1952) 231] evaluate, independently, the number of simple components of the group algebra F G when F is a field of characteristic 0. In this paper we extend this result to fields of arbitrary characteristic which does not divide the order of G. We also compute the rank of the group of the central units of ZG and obtain an alternative proof of a well-known result of Ritter and Sehgal.