Direct constructions of additive codes

A code is qm-ary q-linear if its alphabet forms an m-dimensional vector space over q and the code is linear over q. These additive codes form a natural generalization of linear codes. Our main results are direct constructions of certain families of additive codes. These comprise the additive generalization of the Kasami codes, an additive generalization of the Bose-Bush construction of orthogonal arrays of strength 2 as well as a class of additive codes which are being used for deep space communication