ON THE CHARACTERIZATION OF CYCLIC CODES OVER TWO CLASSES OF RINGS

• 作 者: 刘修生
• 机 构: SchoolofMathematicsandPhysics
• 出 处: 数学物理学报：B辑英文版
• 发表日期: 2013年2期
• 关键词: 循环码 形式幂级数 极大理想 幂零指数 发电机组 代码 残余物 渣场 Finite chain rings formal power series rings
• 基金项目: The author is supported by the Natural Science Foundation of Hubei Province （B20114410） and the Natural Science Foundation of Hubei Polytechnic University （12xjz14A）.

Let R be a finite chain ring with maximal ideal γ and residue field F, and let γ be of nilpotency index t. To every code C of length n over R, a tower of codes C=(C:γ0 ) (C:γ) (C:γi ) (C:γt-1 ) can be associated with C, where for any r∈R,(C:r)={e∈Rn|re∈C}