The Z4-linearity of Kerdock, Preparata, Goethals, and related codes

Abstract

Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson , Kerdock, Preparata, Goethals, and Delsarte-Goethals . It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over Z4, the integers mod 4… (More)
DOI: 10.1109/18.312154

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