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We compute the number of simple components of a semisimple finite abelian group algebra and determine all cases where this number is minimal; i.e. equal to the number of simple components of the rational group algebra of the same group. This result is used to compute idempotent generators of minimal abelian codes, extending results of Arora and Pruthi [ We… (More)

We give counterexamples to show that some results regarding equivalence of abelian group codes, that have been in the literature for quite some time, are not correct. Also, we give examples of special families of abelian groups for which these results do hold.

—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… (More)

In this paper, the minimum weight and the dimension of all cyclic codes of length p<sup>n</sup> over a field F<sub>q</sub>, are computed, when p is an odd prime and F<sub>q</sub> a finite field with q̅ elements, assuming that F<sub>q</sub> generates the group of invertible elements of Z<sub>p</sub><sup>n</sup>. Furthermore, the minimum weight and… (More)

—We consider binary abelian codes of length p n q m where p and q are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds are attained in some cases.

—We consider binary abelian codes of length p n q m where p and q are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds are attained in some cases.

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