四元ZRM码的研究  

Study on Quaternary ZRM Codes

作　　者：裴军莹[1] 王海华[1] 崔杰[1] 

机构地区：[1]苏州大学数学科学学院,江苏苏州215006

出　　处：《数学物理学报（A辑）》2009年第4期891-897,共7页Acta Mathematica Scientia

基　　金：国家自然科学基金(60603016);973重大项目(2006CB 805900)资助

摘　　要：为了讨论二元Reed-Muller码的Z_4线性,文献中先后介绍了两类Z_4线性码,分别记为ZRM(r,m)与QRM(r,m),它们在Gray映射下的二元像记为ZRM(r,m)与QRM(r,m).该文系统地讨论了这两类Z_4线性码.计算了ZRRM(r,m)与ZRM(r,m)的类型,证明当3≤r≤m-1时,ZRM(r,m)是二元线性码,而QRM(r,m)是非线性的;并且,由QRM(r,m)张成的二元线性码恰是ZRM(r,m).最后,对于非线性码QRM(r,m),讨论了它的秩与核.In the literature two classes of Z4 linear codes were defined to discuss the Z4 linearity of binary Reed-Muller codes, they are denoted by ZRM（r, m） and QRM（r, m）, and their binary images under the Gray map are denoted by ZRM（r, m） and QRM（r, m） respectively. In this correspondence, the types of ZRM（r, m） and QRM（r, m） are computed respectively. When 3≤r ≤m- 1, it is shown that the binary image ZRM（r, m） is linear while QRM（r, m） is nonlinear. Moreover, the linear code spanned by QRM（r, m） is proved to be ZRM（r, m）. Finally, the rank and the kernel are determined for the nonlinear code QRM（r, m）.

关 键 词：Reed—Muller码 GRAY映射 二元像 ZRM码 QRM码 

分 类 号：O157.4[理学—数学]