In this work some results are presented regarding the formal structure of codes whose words are built up by means of a system ofn linear forms ink variables (k<n), with coefficients from a finite field.
In n. 1, after a review of several properties of these codes, a different proof is given of a theorem, already proved by I. I. Gruscko, on the linear dependence of the aforementioned forms.
In n. 2 group codes are considered in greater detail, and a distance is introduced and geometrically characterized. By means of this distance a generalization is given of a theorem (known in the binary case), concerning the choice of the coset leaders in the decomposition of the space of alln-tuples in cosets of a code.
In n. 3, finally, a theorem on lattice properties of groups is applied to group codes, and a possible utilization for the construction of codes is pointed out.