We determine all uniformly packed [n, k, 4] codes over GF (2) and we derive a non-trivial necessary condition for the existence of uniformly packed [k, 4] codes over GF (q), where q 2 is a prime power. This condition allows us to classify uniformly packed [n, k, 4] codes over GF (4). As a corollary we obtain a necessary condition for the existence of a projective (n, k, h lt h 2) set S in PG (k1, q) with the property that no three points of S are collinear. A further corollary is a necessary condition for the linear representation of partial quadrangles. © 1982, Oxford University Press. All rights reserved.