[FORMULA] -linear codes: generator matrices and duality

A code [FORMULA] is [FORMULA] -additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of [FORMULA] by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). In this paper [FORMULA] -additive codes are studied. Their corresponding binary images, via the Gray map, are [FORMULA] -linear codes, which seem to be a very distinguished class of binary group codes. As for binary and quaternary linear codes, for these codes the fundamental parameters are found and standard forms for generator and parity-check matrices are given. In order to do this, the appropriate concept of duality for [FORMULA] -additive codes is defined and the parameters of their dual codes are computed.