计算机工程与应用 ›› 2013, Vol. 49 ›› Issue (12): 77-79.

• 网络、通信、安全 • 上一篇    下一篇

环[F2+uF2+vF2]上的[(1+v)-]常循环码

许小芳   

  1. 湖北理工学院 数理学院,湖北 黄石 435003
  • 出版日期:2013-06-14 发布日期:2013-06-14

[(1+v)-]constacyclic codes over[F2+uF2+vF2]

XU Xiaofang   

  1. School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, Hubei 435003, China
  • Online:2013-06-14 Published:2013-06-14

摘要: 研究了环[R=F2+uF2+vF2] 上的[(1+v)-]常循环码。利用环[R]上奇长循环码的生成元来刻画环[R]上奇长的[(1+v)-]常循环码,进而给出了[Rn]到[(F2+uF2)2n]的一个广义Gray映射[φ],证明了环[R]上的[(1+v)-]常循环码[C]在[φ]下的广义Gray像[φ(C)]是环[F2+uF2]上的循环码。

关键词: 常循环码, 广义Gray映射, 循环码

Abstract: [(1+v)-]constacyclic codes over the ring[R=F2+uF2+vF2] are studied. [(1+v)-]constacyclic codes over  [R]of odd lengths are characterized with the help of cyclic codes over [R]. A generalized Gray map from [Rn]to [(F2+uF2)2n] is defined and it is shown that the image under this map of [(1+v)-] constacyclic codes over [R] is cyclic codes over[F2+uF2].

Key words: constacyclic codes, generalized Gray map, cyclic codes