An improved sphere covering bound for the codes with n=3R+2

Let C be a binary code (not necessarily linear) with covering radius R and length n=3R+2. The sphere covering bound on the cardinality of C is improved considerably provided C has minimal distance d>2. Some new results on the function t(n,k) (the smallest covering radius of any binary linear code with length n and dimension k): t(38.6)>or=13, t(47.7)>or=16, t(59.8)>or=20 are given.<
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