环F2+uF2上奇长度循环码的广义RT重量谱

受广义Hamming重量启发,并注意到RT重量是Hamming重量的一种推广,提出了环F2+uF2上线性码的广义RT重量和广义RT重量谱的概念,讨论了环F2+uF2上奇长度循环码的广义RT重量谱。由一个线性码可以唯一地决定其剩余码和挠码,反过来,由其剩余码和挠码并不一定能够重构出原来的线性码。但是当该线性码是奇长度循环码的时候,可以用它的剩余码和挠码重构出该循环码。使用这种方法,得到了环F2+uF2上奇长度循环码及其剩余码和挠码的广义RT重量谱之间的关系。

Generalized RT Weights Hierarchy for Cyclic Codes of Odd Lengthover Ring

Error-correcting code is widely used in the fields of computer security and communication technology.In this paper,motivated by the generalized Hamming weight and the fact that the RT metric is a generalization of the usual Hamming metric,generalized RT weights and generalized RT weights hierarchy for linear codes over ring F2+uF2 are given.The generalized RT weights hierarchy for cyclic code of odd length over ring F2+uF2 is studied.The residue code and the torsion code of a linear code over ring F2+uF2 can be determined by the linear code uniquely.Conversely,the original linear code can not be reconstructed from the residue code and the torsion code.But when the linear code is a cyclic code of odd length,the original linear code can be reconstructed.Using this method,the relation with respect to this generalized RT weights,between the cyclic code of odd length and its residue code,torsion code,is derived too.