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Cyclic and multiresidue codes for arithmetic operations

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2 Author(s)

In this paper, the cyclic nature of AN codes is defined after a brief summary of previous work in this area is given. New results are shown in the determination of the range for single-error-correcting AN codes when A is the product of two odd primes p_1 and p_2 , given the orders of 2 modulo p_1 and modulo p_2 . The second part of the paper treats a more practical class of arithmetic codes known as separate codes. A generalized separate code, called a multiresidue code, is one in which a number N is represented as begin{equation} [N, mid N mid _ {m1}, mid N mid _{m2}, cdots , mid N mid _{mk}] end{equation} where m_i are pairwise relatively prime integers. For each AN code, where A is composite, a multiresidue code can be derived having error-correction properties analogous to those of the AN code. Under certain natural constraints, multiresidue codes of large distance and large range (i.e., large values of N ) can be implemented. This leads to possible realization of practical single and/or multiple-error-correcting arithmetic units.

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Information Theory, IEEE Transactions on  (Volume:17 ,  Issue: 1 )