The rank and kernel of extended 1-perfect Z/sub 4/-linear and additive non-Z/sub 4/-linear codes

A binary extended 1-perfect code of length n + 1 = 2/sup t/ is additive if it is a subgroup of Z/sub 2//sup (alpha) * Z/sub 4//sup (beta)/. The punctured code by deleting a Z/sub 2/ coordinate (if there is one) gives a perfect additive code. 1-perfect additive codes were completely characterized and by using that characterization we compute the possible parameters (alpha), (beta), rank, and dimension of the kernel for extended 1-perfect additive codes. A very special case is that of extended 1-perfect Z/sub 4/-linear codes.