Arithmetic norms and bounds of the arithmetic AN codes

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.