GROUP CODES OVER NON-ABELIAN GROUPS

作者：Garcia Pillado Cristina; Gonzalez Santos; Martinez Consuelo; Markov Victor; Nechaev Alexander

来源：Journal of Algebra and Its Applications, 2013, 12(7): 1350037.

DOI：10.1142/S0219498813500370

• Abelian decomposition
• abelian group codes
• base field

Let G be a finite group and F a field. We show that all G-codes over F are abelian if the order of G is less than 24, but for F = Z(5) and G = S-4 there exist non-abelian G-codes over F, answering to an open problem posed in [J. J. Bernal, A. del Rio and J. J. Simon, An intrinsical description of group codes, Des. Codes Cryptogr. 51(3) (2009) 289-300]. This problem is related to the decomposability of a group as the product of two abelian subgroups. We consider this problem in the case of p-groups, finding the minimal order for which all p-groups of such order are decomposable. Finally, we study if the fact that all G-codes are abelian remains true when the base field is changed.

• 出版日期2013-11