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- W2000394313 abstract "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." @default.
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- W2000394313 date "1971-01-01" @default.
- W2000394313 modified "2023-10-14" @default.
- W2000394313 title "Cyclic and multiresidue codes for arithmetic operations" @default.
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- W2000394313 doi "https://doi.org/10.1109/tit.1971.1054579" @default.
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