a large number of new linear codes achieving the best known bounds $d_q(n,k)$, in particular over small fields, have been constructed as cyclic, constacyclic or quasi-cyclic codes, including the corresponding ones in the non-commutative case (e.g., see [@B0] and [@M2]). For this reason, the main purpose of this note is to study some algebraic and geometric properties of skew constacyclic codes (Definition \[skew GCC\]) and their duals, the latest ones being strongly related to the above minimum Hamming distance $d$ which is useful in error-correcting codes and for some decoding algorithms. Finally, two lower bounds for the distance of these kind of codes are given, together with some MAGMA programs (Programs 1 to 5) as an application of the main theoretical results.

After some notions and basic remarks, in Section \[Sec2\] we recall some known properties of skew constacyclic codes and as a consequence of these facts, we give some geometric properties about the parity check matrices of skew constacyclic codes (Theorems \[GMaruta:2\] and \[GMaruta:3\]), whose columns are composed of orbits of points in projective spaces via semi-linear maps. Furthermore, inspired by [@M2] and [@L], we firstly generalize at the end of Section \[Sec2\] a result about $1$-generator QT codes 