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Lower bounds for constant weight codes

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Let A(n,2\delta ,w) denote the maximum number of codewords in any binary code of length n , constant weight w , and Hamming distance 2\delta Several lower bounds for A(n,2\delta ,w) are given. For w and \delta fixed, A(n,2\delta ,w) \geq n^{W-\delta +l}/w! and A(n,4,w)\sim n^{w-l}/w! as n \rightarrow \infty . In most cases these are better than the "Gilbert bound." Revised tables of A(n,2 \delta ,w) are given in the range n \leq 24 and \delta \leq 5 .

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IEEE Transactions on Information Theory  (Volume:26 ,  Issue: 1 )