有限域上一类等维码的下界

The Lower Bound of Constant Dimension Codes in Finite Fields

等维码凭借其在随机线性网络编码中的良好的差错控制得到广泛研究,对于给定维数和最小距离的等维码所含码字的最大个数目前还没有一般性结果.Tuvi Etzion和Alexander Vardy给出了一定等维码所含码字最大个数的上界和下界,首先利用对偶空间构造等维码C(n,M,2k,k),达到了此类码所含码字的下界,然后具体构造了最优等维码C(7,41,4,2).

Constant-dimension codes become interesting because of their significance to error control in noncoherent random linear network coding. However, the maximal cardinality of any constant dimension code with finite dimension and minimum distance remains unknown. Tuvi Etzion and Alexander Vardy presented the lower bound and the upper bound for a constant dimension code. In this paper, using dual space we first construct a constant dimension code C（n, M, 2k, k） that reaches the lower bound, and then construct an optimal constant dimension code C（7,41,4,2）.