Minimal codes in binary abelian group algebras

2011 ◽  
Author(s):  
Marines Guerreiro ◽  
Raul Antonio Ferraz ◽  
Cesar Polcino Milies
Keyword(s):  
Abelian Group ◽  
Group Algebras ◽  
Minimal Codes

WARFIELD INVARIANTS IN COMMUTATIVE GROUP ALGEBRAS

2008 ◽  
Vol 07 (03) ◽  
pp. 337-346 ◽  
Author(s):  
PETER V. DANCHEV
Keyword(s):  
Abelian Group ◽  
Prime Number ◽  
Group Algebra ◽  
Ordinal Number ◽  
Commutative Group ◽  
Group Algebras

Let F be a field and G an Abelian group. For every prime number q and every ordinal number α we compute only in terms of F and G the Warfield q-invariants Wα, q(VF[G]) of the group VF[G] of all normed units in the group algebra F[G] under some minimal restrictions on F and G. This expands own recent results from (Extracta Mathematicae, 2005) and (Collectanea Mathematicae, 2008).

scholarly journals Invariant ideals of abelian group algebras under the multiplicative action of a field. II

2001 ◽  
Vol 130 (4) ◽  
pp. 951-957 ◽  
Author(s):  
J. M. Osterburg ◽  
D. S. Passman ◽  
A. E. Zalesskiĭ
Keyword(s):  
Abelian Group ◽  
Group Algebras

EXPLICIT DETERMINATION OF CERTAIN MINIMAL ABELIAN CODES AND THEIR MINIMUM DISTANCES

2012 ◽  
Vol 05 (01) ◽  
pp. 1250002
Author(s):  
Pooja Grover ◽  
Ashwani K. Bhandari
Keyword(s):  
Abelian Groups ◽  
Cyclic Codes ◽  
Group Algebras ◽  
Primitive Idempotents ◽  
Abelian Codes ◽  
Complete Set ◽  
Minimum Distances ◽  
Minimal Codes ◽  
Explicit Determination

In this paper minimal codes for several classes of non-cyclic abelian groups have been constructed by explicitly determining a complete set of primitive idempotents in the corresponding group algebras. Some classes of non-p-groups have also been considered. The minimum distances of such abelian codes have been discussed and compared to the minimum distances of cyclic codes of same lengths and dimensions over the same field.

Minimal ideals in finite abelian group algebras and coding theory

2016 ◽  
Vol 10 (2) ◽  
pp. 321-340
Author(s):  
Gladys Chalom ◽  
Raul Antonio Ferraz ◽  
Marinês Guerreiro
Keyword(s):  
Abelian Group ◽  
Coding Theory ◽  
Finite Abelian Group ◽  
Group Algebras

scholarly journals Abelian group algebras of finite order

1950 ◽  
Vol 68 (3) ◽  
pp. 420-420 ◽  
Author(s):  
Sam Perlis ◽  
Gordon L. Walker
Keyword(s):  
Abelian Group ◽  
Finite Order ◽  
Group Algebras

VECTOR INVARIANT IDEALS OF ABELIAN GROUP ALGEBRAS UNDER THE ACTION OF THE SYMPLECTIC GROUPS

2013 ◽  
Vol 12 (08) ◽  
pp. 1350046
Author(s):  
JIZHU NAN ◽  
LINGLI ZENG
Keyword(s):  
Abelian Group ◽  
Finite Field ◽  
Vector Space ◽  
Group Algebra ◽  
Symplectic Group ◽  
Group Algebras ◽  
Symplectic Groups ◽  
Vector Invariant

Let F be a finite field and let Sp 2ν(F) be the symplectic group over F. If Sp 2ν(F) acts on the F-vector space F2ν, then it can induce an action on the vector space F2ν ⊕ F2ν, defined by (x, y)A = (xA, yA), ∀ x, y ∈ F2ν, A ∈ Sp 2ν(F). If K is a field with char K ≠ char F, then Sp 2ν(F) also acts on the group algebra K[F2ν ⊕ F2ν]. In this paper, we determine the structures of Sp 2ν(F)-stable ideals of the group algebra K[F2ν ⊕ F2ν] by augmentation ideals, and describe the relations between the invariant ideals of K[F2ν] and the vector invariant ideals of K[F2ν ⊕ F2ν].

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