On the least covering radius of binary linear codes with small lengths

Using classification of codes with a certain covering radius it is proved that the least covering radius t[17,6]=5; t[17,8]=4; t[18,7]=5; t[19,7]=5; t[20,8]=5; and t[21,7]=6. As a corollary, four improvements on the length function l(m,R) are found. It is also shown that there exists a unique[14,6] code with covering radius 3.