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- Raul Antonio Ferraz, César Polcino Milies
- Finite Fields and Their Applications
- 2007

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 [S.K.… (More)

- Marinês Guerreiro, Raul Antonio Ferraz, César Polcino Milies
- 2011 IEEE Information Theory Workshop
- 2011

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.

- César Polcino Milies, Fernanda Diniz de Melo
- IEEE Trans. Information Theory
- 2013

Let R be a commutative ring, G a group and RG its group ring. Let φ : RG → RG denote the R-linear extension of an involution φ defined on G. An element x in RG is said to be φantisymmetric if φ(x) = −x. A characterization is given of when the φ-antisymmetric elements of RG commute. This is a completion of earlier work. keywords: Involution; group ring;… (More)

- Raul Antonio Ferraz, Marinês Guerreiro, César Polcino Milies
- IEEE Trans. Information Theory
- 2014

Let G be a finite abelian group and F a field such that char(F) 6 | |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)

We consider binary abelian codes of length pq 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 prove a structure theorem for the alternative finite dimensional algebras over a field K, which can be the racional numbers or an imaginary racional quadratic extension, with the hyperbolic property. One class of such algebras is the alternative totally definite octonion algebra over K. We classify the RA-loops L for which the unit loop of its integral… (More)

We consider binary abelian codes of length pq 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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