$${{{mathbb Z}_2}{{mathbb Z}_4}}$$ -linear codes: generator matrices and duality

A code C{{mathcal C}} is mathbb Z₂mathbb Z₄{{{mathbb Z}_2}{{mathbb Z}_4}} -additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C{{mathcal C}} by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). In this paper mathbb Z₂mathbb Z₄{{{mathbb Z}_2}{{mathbb Z}_4}} -additive codes are studied. Their corresponding binary images, via the Gray map, are mathbb Z₂mathbb Z₄{{{mathbb Z}_2}{{mathbb Z}_4}} -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 mathbb Z₂mathbb Z₄{{{mathbb Z}_2}{{mathbb Z}_4}} -additive codes is defined and the parameters of their dual codes are computed.