New lower bounds for covering codes

Some new lower bounds on mod C mod for a binary linear (n, k)R code C with n+1=t(R+1)-r(02 odd) or with n+1=t(R+1)-1(t>2 even) are obtained. These bounds improve the sphere covering bound considerably and give several new values and lower bounds for the function t(n, k), the smallest covering radius of any (n, k) code.<>