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Arithmetic norms and bounds of the arithmetic AN codes

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2 Author(s)

Properties of integers, related to the generation of the arithmetic AN codes, are investigated in this paper. A programmable algorithm for the computation of the binary norm of an arbitrary integer is developed. A table of norms of the natural numbers is generated and from this the distribution of integers of a given norm is found. These results are used to compute bounds on the size of an e -fold or less error-correcting AN code and to derive some further properties of single- and double-error-correcting AN codes.

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Information Theory, IEEE Transactions on  (Volume:16 ,  Issue: 4 )