摘要： 根据有限域Fq上的MDS码与接近MDS码，提出F2+vF2环上的MDR码与接近MDR码，其中包括几乎MDR码。利用环F2+vF2与域F2中加法群的一个同态 ，根据映线性码的生成矩阵证明C是F2+vF2上MDR码，当且仅当q(C)为F2上的MDS码，C是R上的接近MDR码，q(C)为F2上的接近MDS码，并由此给出环F2+vF2上MDR码与接近MDR码的构造方法及具体实例。
关键词:
线性码,
对偶码,
MDR码,
几乎MDR码,
接近MDR码,
生成矩阵
Abstract: This paper proposes the concepts of the MDR codes and near MDR codes over the ring F2+vF2 based on the MDR codes and the near MDS codes over field Fq, including almost MDR codes. Using a homomorphism q of an additive group from F2+vF2 to F2 and the generator matrices of the corresponding linear codes, it proves that a linear code C over F2+vF2 is a MDR or near MDS if and only if q(C) over F2 is a MDR or near MDS. Based on above results, the construction method and the examples of the MDR or near MDR over F2+vF2 are given.
Key words:
linear code,
dual code,
MDR code,
almost MDR code,
near MDR code,
generator matrix
中图分类号:
刘修生, 刘花璐. F2+vF2环上的接近MDR码[J]. 计算机工程, 2013, 39(1): 89-92.
LIU Xiu-Sheng, LIU Hua-Lu. Near MDR Codes over Ring F2+vF2[J]. Computer Engineering, 2013, 39(1): 89-92.