  We consider linear error correcting codes associated to higher dimensional
projective varieties defined over a finite field. The problem of determining
the basic parameters of such codes often leads to some interesting and
difficult questions in combinatorics and algebraic geometry. This is
illustrated by codes associated to Schubert varieties in Grassmannians, called
Schubert codes, which have recently been studied. The basic parameters such as
the length, dimension and minimum distance of these codes are known only in
special cases. An upper bound for the minimum distance is known and it is
conjectured that this bound is achieved. We give explicit formulae for the
length and dimension of arbitrary Schubert codes and prove the minimum distance
conjecture in the affirmative for codes associated to Schubert divisors.
