New codes with the same weight distributions as the Goethals codes and the Delsarte-Goethals codes
T. Helleseth, P. Vijay Kumar, A.G. Shanbhag · 2002
The Goethals code is a binary nonlinear code of length 2/sup m+1/ which has 2/sup 2m+1-3m-2/ codewords and minimum Hamming distance 8 for any odd m/spl ges/3. We construct new codes over Z/sub 4/ such that their Gray maps lead to codes with the same weight distribution as the Goethals codes and the Delsarte-Goethals codes.