منابع مشابه
Idempotents in group algebras and minimal abelian codes
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. Arora, M. Pruthi, Minimal cyclic code...
متن کاملG-equivalence in group algebras and minimal abelian codes
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 minimal abelian codes to be G-equivalent a...
متن کاملConstruction of minimal non-abelian left group codes
Algorithms to construct minimal left group codes are provided. These are based on results describing a complete set of orthogonal primitive idempotents in each Wedderburn component of a semisimple finite group algebra FG for a large class of groups G. As an illustration of our methods, alternative constructions to some best linear codes over F2 and F3 are given. Furthermore, we give constructio...
متن کاملMinimal Binary Abelian Codes of length pq
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.
متن کاملWarfield invariants in Abelian group algebras
LetF be a field of characteristic p 6= 0 andG an Abelian group. For each prime q and each ordinal α we calculate in terms of G and its sections the Warfield q-invariantsWα,q(V (FG)) of the group V (FG) of all normalized units in the commutative group algebra FG when either q = p,Gt/Gp is infinite and F is perfect, orG is p-mixed. Surprisingly, these invariants do not depend on F . This supplies...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1979
ISSN: 0097-3165
DOI: 10.1016/0097-3165(79)90066-9