Classification and nonexistence results for linear codes with prescribed minimum distances
Classification and nonexistence results for linear codes with prescribed minimum distances
复制标题
DOI：
10.1007/s10623-012-9700-8
复制
发表时间：
2014-01-01
影响因子：
1.6
通讯作者：
Feulner, Thomas
中科院分区：
文献类型：
--
作者：
Feulner, Thomas
从一个具有对偶距离的线性[n，k，d]（q）码出发，我们至少可以用构造法Y（1）构造一个具有对偶距离的码。逆构造通过向较小码的奇偶校验矩阵添加更多列来给出所有具有对偶距离的[n，k，d]（q）码的分类规则。同构拒绝应用于保证一个小的搜索空间，这种迭代方法。在此基础上进行完全搜索，我们能够证明16个开参数集[n，k，d]（q），q = 2，3，4，5，7，8的线性码的不存在性。这些结果意味着217个新的上界在已知的表中的线性码的最小距离，并建立在109种情况下的精确值。
Starting from a linear [n, k, d] (q) code with dual distance , we may construct an code with dual distance at least using construction Y (1). The inverse construction gives a rule for the classification of all [n, k, d] (q) codes with dual distance by adding further columns to the parity check matrices of the smaller codes. Isomorph rejection is applied to guarantee a small search space for this iterative approach. Performing a complete search based on this observation, we are able to prove the nonexistence of linear codes for 16 open parameter sets [n, k, d] (q) , q = 2, 3, 4, 5, 7, 8. These results imply 217 new upper bounds in the known tables for the minimum distance of linear codes and establish the exact value in 109 cases.