image4-linear codes obtained as projections of Kerdock and Delsarte-Goethals codes Original Research Article

The Kerdock and Delsarte-Goethals codes can be very simply constructed as binary images under a certain natural map, called the Gray map, of linear codes over image4, the integers modulo 4. We consider the Gray images of linear codes over image4 obtained from the Kerdock and Delsarte-Goethals codes by projection on a hyperplane. For m odd, certain Gray images have the same weight distribution as duals of extended binary BCH codes of length 2m, but are not equivalent to these codes. Inequivalence follows from a general theorem identifying binary linear codes that are not Gray images of linear codes over image4.