A group code structure of a linear code is a description of the code asone-sided or two-sided ideal of a group algebra of a finite group. In theserealizations, the group algebra is identified with the ambient space, and thegroup elements with the coordinates of the ambient space. It is well known thatevery affine-invariant code of length $p^m$, with $p$ prime, can be realized asan ideal of the group algebra $\F\I$, where $\I$ is the underlying additivegroup of the field with $p^m$ elements. In this paper we describe all the groupcode structures of an affine-invariant code of length $p^m$ in terms of afamily of maps from $\I$ to the group of automorphisms of $\I$.
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机译：线性代码的组代码结构是对有限组的组代数的单边或双面理想的代码描述。在这些实现中，组代数用环境空间标识，组元素用环境空间的坐标标识。众所周知，长度为$ p ^ m $且具有$ p $素数的每个仿射不变代码都可以实现为组代数$ \ F \ I $的理想情况，其中$ \ I $是该组代数的基础加性$ p ^ m $个元素的字段。在本文中，我们根据从$ \ I $到$ \ I $自同构群的映射族，描述了长度为$ p ^ m $的仿射不变代码的所有组代码结构。
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