利用对偶空间构造最优等维码

摘要

令Aq(n,d,k)表示射影空间上的码所含码字的最大个数，Tuvi Etzion 等人给出了Aq(n,2k,k)的上界和下界。我们发现当q=2,n=2k+1时上界和下界相等，并利用对偶空间给出了最优等维码(2k+1,2k+1+1,2k,k)的一种构造。%Let Aq (n, d , k ) denote the maximum number of codewords in a (n,M,d,k) code in projective space. Tuvi Etzion etc. have derived the upper and lower bounds of Aq(n,2k,k) .We find that the upper and lower bounds are equal when q=2,n=2k+1, and with dual space we give a construction of optimal constant-dimension code (2k+1,2k+1+1,2k,k).