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A nonconstructive upper bound on covering radius

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1 Author(s)

Let t(n,k) denote the minimum covering radius of a binary linear (n,k) code. We give a nonconstructive upper bound on t(n,k) , which coincides asymptotically with the known lower bound, namely n^{-1}t(n,nR)=H^{-1}(1-R)+O(n^{-l}\log n) , where R is fixed, 0< R< 1 , and H^{-1} is the inverse of the binary entropy function.

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IEEE Transactions on Information Theory  (Volume:29 ,  Issue: 3 )