In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, as linear codes allowing a group of permutation automorphisms which acts freely on the set of coordinates. An algebraic description, including the concatenated structure, of such codes is presented. This allows to construct quasi group codes from codes over rings, and vice versa. The last part of the paper is dedicated to the investigation of self-duality of quasi group codes.
翻译:在本说明中,对线性代码的某些类别作了固有的描述,表明它们可以被更笼统地描述为准群体代码,即允许一组在一组坐标上自由运行的变形自成一体的直线性代码。提供了此类代码的代数描述,包括组合结构。这样就可以从环形代码中建立准群体代码,反之亦然。本文最后一部分专门用于调查准群体代码的自我质量。