A. R. Hammons

TL;DR: Certain notorious nonlinear binary codes contain more codewords than any known linear code and can be very simply constructed as binary images under the Gray map of linear codes over Z/sub 4/, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes).

TL;DR: In this article, the Nordstrom-Robinson, Kerdock, and Preparata codes are shown to be linear over Z4, the integers mod 4, and the Golay code is self-dual.