极大距离可分码的存在范围研究

Research on Existent Range of Maximum Distance Isolated Code

  • 摘要: 引进了F2上矩阵的行间距和极小行间距概念,给出了极小行间距的一些基本性质,证明了在小行间距的两个重要定理。给出了Vn(F2)中Hamming极小距离的两个重要结论,得到了二无线性码(n,k)中存在极大距离可分码的一个必要条件:当k ≥ 3时,n ≤ 3(k一1);当k ≥ 5并且n能被3整除时,nk-1)。同时给出了q元线性码(n,k)中存在极大距离可分码的一个必要条件。

     

    Abstract: In this paper, row distance and minimum row distance of matrix on F2 are presented, and some properties about row distance are given. Two important theorems are proved. According to these theorems, a necessary codition is obtained whether there is a maximum distance isolated code among 2-order (n,k) linear codes:n is smaller than or egual to 3(k-l) when k is bigger than or egual to 3,n is smaller than 3(k-l) when k is bigger than or egual to 5 and n can be dibided by 3.In this paper a necessary condition is also given whether there is a maximum distance isolated code among q-order (n,k) linear cedes.

     

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