The Hamming sphere of radius t with center at the N-tuple x is the set of all Thus, this Hamming sphere contains exactly distinct N-tuples. Prove the Hamming bound for binary codes, that is, which is...

The Hamming sphere of radius t with center at the N-tuple x is the set of allThus, this Hamming sphere contains exactly

distinct N-tuples. Prove the Hamming bound for binary codes, that is,

which is an implicit upper bound on dmin in terms of the block length N and rate R.