  Let K=Fq be a finite field. We introduce a family of projective
Reed-Muller-type codes called projective Segre codes. Using commutative algebra
and linear algebra methods, we study their basic parameters and show that they
are direct products of projective Reed-Muller-type codes. As a consequence we
recover some results on projective Reed-Muller-type codes over the Segre
variety and over projective tori.
