On the character of Sn acting on subspaces of Fqn

Let F-q denote the finite field with q elements. The symmetric group S-n acts on the set, G(n,q) of all linear subspaces of P by permuting coordinates. We show that the normalized character of q the associated permutation representation of S-n approaches the trivial character as n approaches infinity. We also consider the case of the wreath product of F-q(x) and S-n acting on G(n,q) and formulate a conjecture that would yield the asymptotic number of distinct equivalence classes of q-ary linear codes. (C) 2003 Elsevier Inc. All rights reserved.