In this paper, a transform approach is used for polycyclic and serial codes over finite local rings in the case that the defining polynomials have no multiple roots. This allows us to study them in terms of linear algebra and invariant subspaces as well as understand the duality in terms of the transform domain. We also make a characterization of when two polycyclic ambient spaces are Hamming-isometric.

翻译：在本文中,当定义的多圆形圆环和序列码没有多重根基时,对有限地方环的多环和序列码采用变换法,这样我们就可以从线形代数和无变子空间的角度来研究这些代数和无变子空间,并了解变形域的双重性。 我们还对两个多环环环境空间是Hamming-isomit 时进行定性。