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Byte-organized memory requires an error control scheme which can handle errors involving one or several entire bytes. A special parallel nonbinary single error correction and double error detection SEC-DED block code is constructed by dynamic programming. This code is optimum in the sense that it lends itself to a simple and high-speed hardware implementation either in binary or in quaternary logic. A double extension field GF(22m) of the subfield GF(2m) is then introduced. As a design example, a(80,64) SED-DED code in GF(24) is constructed.