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Дата последнего поиска статьи во внешних источниках: 7 сентября 2016 г.
Аннотация:New families of perfect codes for an additive transmission channel, are presented. Perfect codes in a channel with errors of the form 0 → 1, 1→ 0 are a well-known object of study in the classical theory of error-correcting codes. Hamming codes, which correct single-bit errors, are the perfect code for additive channel. The first order neighborhoods generated by the code points do not intersect and cover the entire set of binary words. This is a standard necessary condition for the existence of a perfect code in additive channel A, namely the cardinality of the first-order neighborhood or, equivalently, the cardinality of A must be a power of two. It was also proved that if an additive channel is generated by the hamming code V, then the unit ball is a perfect error-correcting code for the additive channel V.